Any suggestions what to do about my mom refusing to socialize in independent living?

I went through the same thing with my mother. She said she was walking her dog when in reality she relied on pee pads. That worked to some extent but he then seemed to have decided any floor treatment, like her oriental rug, was a pee pad. She has always been very active and social but she was just sleeping in most of the day then watching tv. She has improved greatly and is enjoying life again but it has take a team of wonderful people to get her to that point.
First I lucked out and found a great geriatrician who started working on her physical issues such as better control of diabetes. At my request she also tested her for depression and cognitive issues and found she was dealing with both. She then started my mother on antidepressants. She has been following my mothers health closely, in fact I have to go shortly to take her to an appointment.
I was lucky again when a friend of mine, who is an RN and had lost both of her parents a short while before, offered to spend a few days with my mother to catch up on cleaning and other projects and to let me know how she was really doing. My mother doesn’t like one of my dogs for the way he barks so I don’t spend nights with her and she lives two hours away. I think the fact that it was a friend of mine who had visited her on occasion helped a lot since she had been adamant that she did not need help. We then hired my friend to spend a few days each week with her.
When it became apparent that she needed to be checked daily to make sure she was taking her meds we hired another, local, RN to help her on the other days. She really objected and still says she doesn’t like her but they seem to get along when together. My mother has always had trust issues. The new woman started to take her to the movies at the senior complex’s main building (my mother has a cottage) and also looked for other things to do with her. Both of them walk her dog and are encouraging her to join them on the walks when the weather is nice. My mother now asks them what the plans are for the day when they come and even ate at the dining hall after a movie and got to talking with some other residents! It has taken two years to get to this point and a wonderful team. The doctor recently said that she was really at the stage for assisted living but that she seemed to be good for now. We do have to keep reminding her that without both caregivers she would have to be in assisted living and that helps her accept the help.
In summary I think that finding a good doctor to control all medical issues as well as test and treat her depression, finding daily help for her who are also willing to walk her dog, a lot of hard work, and, in my case, a lot of luck in finding good people has made a huge difference. Nothing will stop the cognitive decline but she is doing things and enjoying life again. One last note, she does try to discontinue the antidepressant occasionally since she says she isn’t depressed now so we keep having to remind her that she isn’t depressed because she is taking the meds! I am on them myself and I know how hard and fast the depression can return if you stop.
Good luck!

Well obviously your mom is no longer independent, so time to move her into an assisted living facility. By you continuing to go and clean up after her, only helps keep the illusion up that she's still independent.
Other than her being depressed it also sounds like there is some type of dementia going on, so definitely get her to her doctor sooner than later to find out exactly what she and you are dealing with.

It sounds like mom's mental and physical status have declined to the point where Independent Living (and having a dog) are no longer possible.

Does she have a diagnosis of cognitive impairment? Depression? Dementia?

I would start by getting her to her PCP for a checkup and discuss possible referrals to neuropsych and psychiatry.

Has mom had a physical lately?
If not it is time to schedule one.
Send a note to the doctor (use the portal to communicate so you do not have to discuss your concerns in front of mom)
this could be :
Depression
Cognitive decline. And this could be from any number of causes.
Underlying illness.

If she can not manage the dog then hiring someone to come in a few times a day to walk the dog would be the kindest thing to do for the dog. maybe the person walking the dog can get mom out as well. I have long thought that there is a risk of falls when a person with a walker, cane or other mobility problems has to walk a dog.

Hold off your assumption that "she's completely capable" until after she sees a doctor.

As others have said , sounds like depression and/or cognitive decline . Get her to the docs for testing . I also believe she belongs in assisted living . If she is allowed to keep the dog and you want her to keep the dog , the dog will need to have a dog walker come regularly . IMO though , I don’t think it’s fair to the dog . He needs an owner who is competent to interact with the dog and be able to respond to its needs . No one with a walker should walk a dog. That’s a recipe for disaster .

The problem has to do with mom's cognitive decline. As others have said, she needs an evaluation. Letting her dog soil her home is not normal behavior.

After she's evaluated, you may have to make choices. One of them should not be inviting her to come live with you. Many have thought that was what would help an elderly parent, and many have found themselves miserable, their families torn apart, their finances wrecked, and the parent in even worse shape. Don't do that.

If her community has continuing care, check out the memory care unit. She may need to be there.

Good luck with all of this.

Your mom needs a full work up at the doctor.
You need to realize her social life is not your responsibility.
Not wanting to socialize with others there is not my concern but no longer walking the dog is a big red flag. Hire a dog walker at the least.
She is no long Independent. She needs assisted living.
Do not even consider having her move in, it will not end well.

About answering the door without even greeting you...

I too have experienced behavior from my mom that felt like extreme discourtesy: for example, single-word imperatives--"blanket"--instead of polite sentences--"could you hand me my blanket?" 

Also, I set up some smart lights and she seemed sort of annoyed about having to say "hallway light" instead of just "light." This too I processed as rudeness/ingratitude. 

But recently, after a very bad 72 hours, when I was deeply exhausted, I realized that speaking even one extra word (and just speaking at all) actually takes an enormous amount of energy.

I'm better rested now but trying to hold onto that memory since at the time I felt like it gave me important insight into how my mother speaks / doesn't speak.

Not sure if that helps at all or is relevant to your situation, but I'll post this just in case.

I agree with the posters who urge you to get your mother to her doctor. Review the change in her behavior with her doctor and they should run some tests which will probably lead to some changes to her meds. We went through a very similar situation with my mother (who turns 75 this year) and we found out she has dementia. Doc set her up with mental health services, tweaked some meds, and we have seen a huge improvement. We're not looking forward to the road ahead but we're happy things are better for now.

In hindsight, one of my mother’s first symptoms of her cognitive decline was refusing to socialize. An extrovert, she had loved to be the centre of attention. She made up all kinds of excuses - other seniors were too old, she didn’t like them anymore, they didn’t know her history so she couldn’t discuss her life with them. She wanted me to be her sole source of entertainment. But if I forced her into a social situation, she lit up. She was the belle of the ball at her brother’s funeral.

Now, she’ll complain that she’s lonely and nobody visits, but maybe 1 out of 4 or 5 times tell us to leave the moment we arrive, because she doesn’t feel like having visitors. You may not be able to fix your mother’s social life.