When I had to have a similar conversation with my grandmother, I sat down with her one-on-one and asked her straight out about her plans. What she had set in place for when she could no longer take care of herself (physically). We had a long discussion about estate planning, legal documents (power of attorney, living will, etc.), etc. I know which banks she works with and where in her house to find the information on the accounts, but I don't have any idea how much money she has. I called her attorney (with her permission) and let him know that she and I had had a conversation and that he needed to be sure she had XYZ documents prepared. I made it clear to her that moving in with us is not an option, and asked her what plans she had. Then I started presenting options (some of which I knew she wouldn't like). When she didn't like my options, it spurred her to do some research on her own. So now she has a plan in place.
Personally, I would be less concerned with your mother and more concerned with your sister. Your mother has the property (which I assume is in her name?), which she can rent/lease/sell were she to run out of money. The conversation you should have with your mother is what she's planning to do when she can no longer physically take care of herself - is she going to expect your sister to do it? Estate planning types of questions are also in line - does she have a will? Does she have a power of attorney and a medical power of attorney? Living will? All important documents for all adults, but particularly seniors to have. You don't necessarily need to know the contents of the documents (unless you're her PoA or her executor), but just that she has them.
For your sister, this one is a lot harder. Tough love is probably the only way to go there. You don't have any responsibility to support her, and you've made it clear that you're not going to. So you just have to stand by that for the sake of your little family. It's not the easiest thing to do, but you have to do what's right for yourself and your kids.
Ultimately, you just have to remember that they're adults, and you cannot control their lives or behavior. They have the information they need, and if they choose to live with their heads in the sand, you can't stop them.
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