My 94-year-old father just came home from rehab. Any advice?

If you think both need to be in AL
If you think that is the safest place for both of them
OR
If you think they need to have caregivers most of the time
If that is the safer option for them in order to remain in their home
you and your siblings have 1 option....
BACK AWAY
You are enabling them to remain where they are not safe by propping them up and giving them a false sense of independence.
The difficult thing is to let them realize that they can not be on their own.
Give them the option of AL or having caregivers some in for a minimum of 5 hours daily. Go by their schedule. If both are ok getting up in the morning then their caregiver can come about 9 am. If they need help then the caregiver comes earlier.

Getting to your question
Medical transport can get dad to the doctor.
Dad's doctor can order a wheelchair (surprised this has not been done) the doctor can order all the equipment that dad needs to remain safe. Hospital bed, wheelchair, walker. And other equipment can be borrowed. Many places have "lending closets" with shower benches/chairs, risers for toilets.
If it has not been done yet get someone in to put up grab bars near the toilet, bathtub, shower. (If there are towel bars I would remove them and replace them with a grab bar, many people will instinctively hold on to the towel bar for stability/support)
Put motion sense lighting in hallways, stairways.
Remove carpeting if you can. With a walker or wheelchair carpeting can be difficult to go over. Not to mention it is a trip hazard.

And an off comment about rehab. It does not sound like he should have been discharged. It does not sound like it would be classified as a "safe discharge" particularly if they saw that "you were barely able to get him in the car"

I read your response "My sister and I are trying to make this happen"! That is the core issue, you are doing everything they cannot, they are unable to care for themselves anymore.

They both need to be in AL and as long as you two compensate nothing will get better.

I certainly would push for a DPOA and consider backing off so they will understand that they need to be moved to a place that has 24/7 aid and a clinically trained staff.

Good Luck.

You can hire a transport company. We used one to get my dad from rehab to home. They can provide a wheelchair if needed or if Dad already has his own he can use that. If I remember correctly my Dad had to be able to transfer on his own if needed. The same company also took Dad to a doctor appt while he was in rehab. They were strictly transport so they got him to the appointment but they don’t stay there. You call them when you’re done.

I don't know your history (too many posts to go through), but it sounds like your father needs more care at this point than you are able to provide.