If they are physically able to drive around, and go eat out, and help with the household chores, I would say they're still quite independent, despite being disabled. I would also say that at this age, they are probably very well set in their financial ways.
Would they consider paying you guys rent, and still helping out with the household needs, seeing as their only daughter is in poor health, and there's a lot of little ones needing care? Not for part of the rent, but just because they're her parents and you guys need the help?
If they would be open to that, I would consider going back to them paying rent, them helping with the household as much as they're able and willing to do, and let them run themselves into bankruptcy if that's their choice. Once the credit cards are maxed, they won't have much option to keep spending over the monthly income. If they eventually start stiffing you for the rent, at least you've been receiving it up until that point, and they can continue to help with the household needs.
Long term, as their disability care needs increase, they will have no assets and limited income, and will potentially qualify for state assistance with in-home care. I agree that, when it's possible, it's good to have the extended family together, especially at this point, when they can help, and your wife is their only child. If they were somehow siphoning off money from your income, that would be different, but it doesn't sound like that is the case, at least at this point.
If they eventually need to go to a nursing home, the state will pay for that. They probably won't be able to go to a fancy place, or assisted living apartments, but when it's a nursing home for foster facility that is needed, the state will cover it. At least this is how it has worked for us in Oregon. We just went through this process with my mom over the last year. Towards the end of her time at home, she was able to have a "helper" come in (not a nurse, but a home assistant kind of gal) to wash dishes, drive her to the store or go shopping for her, clean the house, help her bathe, etc. Then, when it was time, she went into a foster facility and the state pays for that. My brother is handling the details, but basically the state will take her social security funds and then they pay for everything for the foster facility.
Whether they stay or move out, their debts are their own concern, and will not obligate you financially, unless you co-sign for something with them. In fact, if they are insolvent when the time comes, obtaining assistance for long-term care needs and intermediate home-care needs will likely be easier. Sad but true.
I wouldn't even bother to try and straighten them out financially, help them or encourage them to sell the car, etc. It is what it is. Quite honestly, I would give them the grace to be financial idiots, and be grateful that you can all assist each other during this time period, and that they can help you and your wife right now. Accept any rent that they are willing to pay, request and accept and be grateful for any household help they can give, and let them blow every other penny they get. :-) Long term, your relationships will be sweeter, and life will get easier as the kiddos get older (I have 4 under 8 right now, and just got off a 3-year health nightmare).
I will be interested to follow your journey! Good luck!