I think I can speak to this... On a personal level as well as professional level.
I have been going through the same thing with my parents... all last year into this year.. Thankfully neither of them had Covid, they just had everything else health related, my Dad was in ICU for over a week, then several days on another floor, then went to the nursing home for rehab, then back to the hospital, then back to the nursing home, I picked him up the day they closed all the nursing homes. My mom, 4 different trips the ER and all resulted in at least 1 or 2 nights stay. Right now things have leveled out, and they are both doing much better, both have had both vaccines each so they are protected... My Dad was non-compliant with everything... would not wear the back belt, did not want to take the med's... did not want therapy, Same thing with my mom not listening to what the doctors said... Then I went to the doctor with them, and found out that they were not telling the doctor what was going on, So once I started filling the Doctors in on what was really happening... Things started changing... One doctor said to my Dad if we don't know we can't help you.
My dad got all mad at me, which by that point I really did not care if he was mad or not... Once my Mom started feeling better, and getting the right med's things have turned around, it has been a slow process yet progress very day...
Professionally- I worked in Long Term Care and Rehab facility, Alzheimer's Units, Assisted Living, and Independent Living... In accessing my parents they need would be so much better off in a Independent Living facility, so they would not have to worry about meals, cleaning, rides to the Doctors, activities and such.. they still would have their own apartment so still have independence, just so much less to deal with. They live in their home right now. Just with what you have posted her, that Assisted living with your FIL having mobility issues, and MIL having the beginning of dementia, would be they way to go. You might want to approach him as it would be better for your MIL.
Personally - As my parents care giver, medical and financial POA. Which I gladly accept and I'm honored that they chose me to be the one to do this for them. As a child even adult child, you feel that there are boundaries that you should respect, and after all they are your parents. At one point I felt that I was drowning with trying to deal with all my Dad shenanigans, and my mom depression and anxiety, as well as the medical and financial issues that were cropping up, then throw in this whole big mess with Covid... I called a friend that is a elder care therapist, and talked to her for a bit... She really helped me understand what was going on with them. As well helped me face what was happening, and gave me some tools to deal with it... First and foremost she told me that I had to have a conversation with myself and honest conversation with myself, on what I can and can not do... She said at first kids will say oh sure you can live with us, never realizing whats to come... She said once I had really been honest then I need to have a direct conversation with my parents, and tell them what you can and will do to help them and what you can't and won't do and stick to it... She said if you waver, they will see it as a sign you will change your mind. None of this is easy to deal with. Yet the sooner you deal with it the better off you all will be...
You have to be completely honest with your DH, tell him how you feel and ask the hard questions and look at the long run, not just right now, setting aside the emotions... Make a list of questions, how will this effect each of you, physically, mentally, and financially... How is this going to effect your marriage, if things drag on for years and years. If they both move in..... Where will you end up, and it will take a toll on you.
I also want to touch base if your MIL has slight dementia, this is something that does not get better, and are you equipped to handle it, in the long term. I hope you don't think that I am being crass, If your FIL was to pass away, and they are living with you, how will you handle your MIL needs. As well with Dementia and Alzheimers, as the mind start to fail, so does basic care of oneself, eating, dressing, sleep patterns, showering, using the bathroom which is another whole thing, from accidents to having to have someone change adult diapers, as well could your DH do this for his mom, help her shower or change her... as well are you comfortable doing this for the both of them... these are all things that could happen...
Your FIL has great mobility issues, which is a huge risk... god forbid he falls, what about showering elderly people get to the point that they don't want to shower, because they are afraid of falling, and again things like using the bathroom comes into play. As well if he or she for that matter was to fall, how are you going to get them up? If your FIL is demanding that is something that is not going to change.
As well you have to think about their safety in your home, grab bars in the shower, shower chairs... furniture placement, even things like throw rugs or kitchen mats, Meal times, and if you both work who is going to do all that. If you guys want to travel or just spend the day out shopping who is going to care for them... What if you want to have friends over for dinner, they will be right there...Right now it might be okay, looking ahead it might not always be okay... how will you handle that if it happen...
Then thinking of the financial impact this will have on you... adding to more people in the house all day will effect everything, more laundry, more groceries, more meals to make, more cleaning of the house, light and water bills will go up. Again not wanting to be crass, I would assume that they will help out in this area, with that comes this thought, and I say this as my good friend went through this with her FIL, Well I give you "blank amount a month" I pay you to take care of me, so I expect this and this and that. Wants he meals at a certain time, and wants lights out like at 7:30.. We were over there for a birthday dinner, and were sitting out on the deck just talking just the 4 of us, it was around 7:30 and her FIL came out and started telling us to be basically go home, he was trying to rest and this was his house and he pays all the bills, and we kids should have more respect... and yes he has always been that way... He had been living with them for 4 years at this point. My friend left her DH, she packed up that night and left... she stayed in a hotel for 2 weeks, and rented a studio apartment for 3 months. Her DH moved his Dad into an assisted living facility... Which he is still living at 3 years later, and still is as grouchy as a bear with a thorn in his paw. She said that she had misgivings from the very start, but did not want to hurt her DH... and thought she could just deal with it.
I sat down with my parents, and to be perfectly honest I was a nervous wreck, yet I knew that I had to be honest with them... I had to let them know what I could do so that they could plan accordingly... That I loved them very much, I needed them to know where I was at, and So I just told them what I was able and willing to do, and what I wasn't able to do. They kept trying to get me to commit that my mom could live with me, if my Dad was to pass away first... Which I stood firm and told them that was not a option. I will say that they hint around all the time, seeing if I will give in or change my mind... Which I stand firm... When they start in about the house and all the stuff, like a new air conditioner, or having the house painted, and new dish washer... I ask them well are you ready to do something different... to which the answer is no... then I change the subject... To go back and forth to my parents house is 130 miles round trip.. I try to go every other week to see them, I take them a home cooked meal, and some treats, and I talk to them everyday... I know that eventually I will have to step in and just take over and make the decisions, right now we are in a sweet period... I pray and hope it last for a while.
I hope you don't think that I was trying to make you upset, at first after I talked to my friend that therapist, I kinda thought she was harsh, the more I thought about it, and talked things over with my DH, and DD... I realized she had given me alot to think about, Good solid information, and tools to help me reach the conclusion that I already knew... really what that was from the very beginning, it gave me the knowledge and courage to move forward and put it into words.... Each person has a different set of circumstances, so everything is different. I know this is hard, and I'm truly sorry that your going through this... sending hugs and prayers to you and your family...