I think you just have to keep living your boundaries, which is especially challenging when living under one roof with others. The first problem you mention - the birthday dinners - doesn't seem like a problem. "Because that's always been how she has treated DH for his birthday - to pay for both of us, since she wouldn't take only him out to dinner when we are a family unit." If she still doesn't understand, well then tough. And it sounds like the dinners may be coming to an end anyway if your MIL is not able to get out of the house much due to declining health.
Regarding the housekeeper, I'm curious if the fee went up due to extra cleaning? If so, then it's reasonable to expect SIL to pay. If not, then I'd say she benefits from the situation, but there's no reason to ask her to pay 1/3 of the time. That doesn't mean she shouldn't clean up after herself regardless of whether she pays for the housekeeper. I'd stop doing her dishes and remind her they are needing to be done, for example.
Since a family meeting isn't possible, you can meet with her separately to discuss common household agreements, like advance notice if either of you will have company, maintaining general cleanliness, etc. As you said, she's never lived with anyone, so she may not realize she has to compromise. If she refuses, though, don't feel you have to back down. Ask her to clean up her belonging, clean her dishes, etc.