We have a dilemma that I can’t seem to fix. Any advice?

"No" is a full sentence.
You've tried the strategies that often do work, with reasonable people.
However, many reasonable folks have unreasonable views of their own needs/likely life span. So, what happens next will not be to their liking....but they refused to cooperate with the easy way. Sometimes stepping back and letting them rely on others (the kindness of strangers and the social services and public safety system) helps them realize that their daughter actually had a lot of good ideas!
I'd make a list of numbers they can call if they need help
the local Council on Aging,
home delivered meals program
the local aging access services point - the Council on Aging will know about this - they often can give resource suggestions, even if your parents are over-income to receive subsidized help at home.
The non emergency number for life assistance at home - less sirens and drama than 911 if someone falls, but includes paramedics who assess and can encourage/insist on trip to ER if indicated. Sometimes this is a county dispatcher, usually there is a local phone number for police or fire dept.
Let their MDs know you are unavailable for a month or so.
Then, let them be on their own.
Don't go there, even before your surgery. Refer them back to the phone numbers, suggest that they need to figure out what to do as they don't need help, etc.
You can call and check on how they are doing....and only that.
If you can't reach them for a few days you can ask the police to do a well being check.
If their mail is delivered right to their house the postal delivery person might notice it is not being taken out of the box..or that newspapers are piling up on the doorstep.
Is there a neighbor who might let you know if things were awry....
even if everything falls apart for them, call their police/fire and ask them to go check ....they can access the emergency systems and maybe also file elder abuseneglect report if they are concerned about what they find. It is not accusatory, it is the way to get services focused on your parents without requiring you to be there.
You need to focus on you. They won't be around to take care of you when you get old, and if they end up in nursing homes all their money will be paid out for their care. If you do receive money from their estate. great. but not to count on it.
Take care.

Yep, been there! My dad was 97 and living in a 3 story, 4 bedroom house AND he was blind. According to him, he was doing just fine. I, however, was arranging meals (even to the point of arranging Uber Eats deliveries while I was in Europe) because he refused the Meals on Wheels delivery and fired (actually was so hateful she quit) home assistant that I had arranged to provide him extra housekeeping and dinner preparation. He'd been on the list for a lovely assisted living apartment but each time one was available he would tell them to give it to the next person (I didn't know this for a long time.) I only lived 5 minutes away so when I was home it was constant requests for small things which then led to big things which then led to more work than I could possibly keep doing. The final straw was when I had to fly home one day after going on vacation for a small, but annoying problem he had and no one else was going to be able to solve it. Finally, I just told him that he had to move; I wasn't helping any more except for one grocery trip a week and doctor's appointments, and if I was out of town then he'd have to solve it himself. He told me he'd move to the assisted living apartment but there wasn't one available. I'd already checked and it seems he had removed himself from the wait list and that they actually did have a smaller unit currently available. I told him to move to the smaller unit because I was DONE. He begrudgingly moved and finally admitted he should have done it a long time ago. Moral of the story: You know what needs to be done but you'll never be able to get them to move until you stop making it possible for them to keep up the pretense of being "independent." Just stop helping maintain this charade. No more weekly trips, no more emergency calls, and stick to it. It's called "waiting for the catastrophe" which will happen eventually but it seems to be a necessary part of making the assisted living decision for many of our parents.

You have done as much as could possibly be expected. Now back off and deal with your own health issues. Also it would be good if you tell them in great gruesome detail what your health and surgery entails. Elderly people seem to consider anyone younger to be in good health and able to take care of them. Moan and groan a bit while you tell them you flat out can’t help now. Clutch your side and faint. Then these two selfish people might stop playing you. Because that’s what they’re doing.

Bliss, first off, you don't have a dilemma you can't fix. Your parents have a dilemma that they WANT you to be the fix for. Stop owning their problems.

Many of us have or are facing the propped up independence of our parent(s). It just sucks! So big warm hug for you.

I would not do anything the help they had you fire did or would do. Nope, not cooking to have 14-21 meals x2 in the fridge or freeze while I am here, that was what food delivery was for. Nope, not scrubbing your toilet, doing your cleaning or anything else the home care help did. Doesn't make them happy? Well, you are the ones that say you are independent and don't need those services, so I am not doing what you say you can do.

As long as you prop up the delusion of independence by giving them one or two days a week, they don't have to change anything. Stop participating in the charade and see how things evolve.

I, firmly believe, we are ALL responsible to have plans for our old age and that doesn't include dumping ourselves on our loved ones. Time for them to face the reality and live with their choices.

Unfortunately I have learned by experience, TWICE, that when you KNOW that a move to residential care is all but a done deal, it’s better for all concerned to get the deed DONE, without intermediate attempts to delay the event.

Your needs are very important, and being stress impacted, make them even more so.

“I hate to do this Mom and Dad, but my rheumatologist has told me that I can ONLY assume responsibility for myself, and YOUR doctors have told me that YOU need more are than you can receive while living where you are right now”.

“If I have to involve a lawyer to convince you that you must live closer to me for a while it will COST YOU A FORTUNE”.

“LUCKILY, there’s an ADORABLE place, a lot like a hotel, for you to come to RIGHT NEAR ME, so we can all figure out what to do after I’ve healed and started to feel better.”

You will notice that there are some “truth bends” in this script, and you can most certainly adapt AS YOU GO, but bear in mind that their SAFETY and WELFARE and in this case YOURS, are more important than useless facts.

You are confronting a painful but ESSENTIAL TRUTH- the THREE of you need a major change, and you need to be the motivation.

Good Luck!

Make your help contingent on them accepting other help. Make it clear you cannot do it all. If they refuse all help other than yours leave them to it and let them prove to themselves that they can’t handle it all on their own. It sounds harsh but unfortunately it’s the only way to get through

No mom and dad, I can not be the answer to your needs. You seem to forget that I'm not a kid anymore and I have my own health problems, I will not build my life around you and your needs. Repeat, repeat repeat.
And it won't hurt them to do without a little bit if you can't make it for a week or two, sometimes a lesson needs to be learned first hand.

If she wasn't my 'mother' I wouldn't even go once a fortnight btw. I wouldn't visit at all.

Bliss--welcome! I hope you get some good answers and support.

First, you are VERY LUCKY that mom & dad have funds. Whether they WANT to spend them or not isn't germane to the subject--they HAVE to spend them for the care they need. Probably they want to keep as much as possible so you can have a nice inheritance--but I assume you are like a lot of us--we'd rather have our LO's safe and cared for in their declining years than have any kind of inheritance.

Mom and Dad aren't going to like it, but you are going to have to be tough with them. Sit them down and explain to them, as you did to us how you HAVE TO take time to care for yourself. Believe it or not, your parents still look at you as a fit and spunky 30 yo--and I fathom you are not in your 30's.

Show them the facility you liked best and give them the choice on how to decorate their living space and really play up how NICE it will be to have 3 meals each day without worrying--activities and things to do. It will not all be on YOU. (Yes, I am kind of suggesting you guilt them).

Let them find out what it was like before they had some in home care. (sounds like they already got that in motion!)

Always respect them as your parents, but often, that role of parent/child gets kind of reversed when the parents aren't making good choices.

You need to take care of you and leave them to their own devices. Do not do anything for them anymore so they can see they are not independent. If you keep helping them they will never accept it.

I hear your dilemma. I think it's time to use the NO word which sounds like it will be very hard for you to do. (I get this btw, but in saying NO to my elderly parents about this and that has been super freeing for me and when I see them now it's not resentfully)

2. Want to stop home instead care and meal delivery since I come once a week.

What would they do if you didn't/couldnt come one a wk?

Decide what you can and will do, not what they want you to do. You dont need to justify/explain what you can and will do. If you sense that an explanation/justification for what you can and will do is required by them...thats a red flag in my book.
In my opinion what you can and will do for them is met with a thank you. Full stop. Ironically if it is met this way with a genuine full stop after a thank you...we do more for that person...authentically. It just happens. Put you and your needs first....unapologetically.
I have had to assert firm boundaries with my parents, particularly my mum...she is very narcissistic/abusive/critical/demanding. She would have me 'helping' her every day and it wouldn't be enough! I go every 2 wks for about an hour. I dont think she's grateful for this and I am pretty sure she slags me off to other family members saying I dont do 'enough' for her. So be it. I'm doing me.

"Makes me so mad! I’m feeling a bit defeated, " Take back your power, own your feelings. Its empowering and work out why you feel so responsible.
Good luck!