First, you are great to be so concerned. You are doing the right thing to want to help and to see how stressed MIL is getting.
One thing you can do for her: Find her some peers with the same issues.
Your husband and his sister can find some local chapter of the Alzheimer's Association or any other organization that works with families of Alzheimer's patients. Also check with all the local hospital systems--larger hospitals have extensive support and advice programs for families and caregivers of the chronically ill.
What you're seeking is a weekly support group for the families of Alzheimer's patients -- groups MIL can attend where she will meet other people who are in exactly her same situation and who can tell her what to expect better than anyone else can. The first few times, maybe you can drive over -- I know it's two hours -- but one of you can watch FIL while she goes to the first meeting. One of you may need to TAKE her and sit in the car and wait for her to drive her home, so she cannot make excuses about not going. She needs a peer support group to give her ideas, advice, emotional support. Your husband and his sister also could benefit from support groups in the areas where you live, so they can learn more about what is going to happen.
Your husband should get the doctor to meet with MIL, your husband and his sister and explain the progression of this disease and what to expect. This is crucial. If the docs are just tossing meds at dad and sending him home, but not helping MIL connect with support groups, giving MIL informaiton about home care options, etc. -- then your husband and SIL need to get very assertive with the medical professionals about getting more realistic advice to MIL.
If MIL and FIL are on limited income, it's time to explore at what point they will be eligible for Medicaid (though they may have to spend down assets first, they should be able to keep their home). Are they on Medicare at all? What will and won't it cover, if theyr'e on it? Do they have a Medicare supplemental insurance? (We were surprised how much my late mom's Medicare supplemental insurance covered when she really needed help.) Have husband and SIL got legal, medical and financial powers of attorney for both their parents? If MIL dies suddenly, does some adult have legal power of attorney over FIL? It's essential to protect them both. Maybe your husband and his sister have done all this and if so -- excellent. If not, it's time. MIL won't like it; if she's in denial this will be painful for her; but it has to be done.
I get the idea of keeping him at home as long as possible -- in his familiar environment he is perhaps likelier to do better, longer. So look at home assistance of some kind, and again, you and husband and SIL may need to set up funds of your own to help with that. Call their insurers and find out what might be covered even minimally, too. You mention getting help from churches but I would start first with the local city or county government; they often have a "council on aging" or office that handles senior citizen services; they won't provide caregivers directly but should have a lot of informaiton on local services and businesses that do. Also, in our area there are community centers that are aimed mostly at serving older citizens, and they always have flyers, information etc.
I know you said MIL has researched this but you and the other adults might be able to find more than she did.
Also, please, please start looking right now at long-term care homes that specialize in Alzheimer's patients. It may not be time to put FIL into care yet, but you don't want to be doing rushed research when you suddenly find MIL just can't handle him any more. You may have to commit to having the adult children pay for some of this, frankly.
Not to be alarmist, but you need to be aware that her safety could be at risk eventually, even if it's not right now. He can be the sweetest man in the world and this disease can make him do things that are dangerous to her, himself and their home. My aunt's boyfriend nearly burned down his house by accident; our neighbor's husband, the gentlest man I ever knew, had moments of lucidity when he told his wife to put him into a care home because at other times he was so inexplicably angry that he feared he would hurt her, not even knowing who she was. And even where there are not risks like those, it just is so stressful on the caregiver spouse to deal with once the disease really progresses beyond a certain point.
Our neighbor was so reluctant to place her husband in a care home, but she also realized that it was a relief to her. Again, he did stay at home with her caring for him for a long time, but eventually her own health was suffering from the caregiving. She was much better, and less resentful toward him (much as your MIL is resentful at times toward FIL), and was able to have very good visits with him, once she was no longer his 24/7 caregiver and was able to get some respite for herself.
Your MIL may not be at that point yet or for a while to come. I'm just saying, consider planning now so that you younger adults are ready to help her get FIL into care when the time comes. And for right now, I'd help her get to a support group where she can hear from people in her situation.