I hope I don't regret this, but I'll give this a go. I've seen your posts. I've never responded because you come across to me as aggressive, argumentative and basically intimidating...I was extremely apprehensive of responding and ending up in some sort of disagreement with you.
I'm sure I haven't read even most of what you've posted. But the posts I have seen all seem to be basically the same thing... You want to move. Your mom agrees and then changes her mind. Sometimes she changes her mind on her own. Sometimes she changes her mind because your sister interferes. You think it's not fair. You think they're ruining your life.
I'll respond to the details based on what I've read or what I recall. If I have something wrong, it is an innocent, unintentional misunderstanding. Feel free to correct me but I would ask that you do it with some degree of kindness. There is no reason to blast me, talk down to me, try to make me feel stupid or be passive aggressive with me over an unintentional misunderstanding. Please remember that I also have PTSD (as do others here on the forum) and opening myself up to that kind of response from you is basically risking my own sense of safety and stability in order to attempt to help you. Even if what I (or others) offer isn't helpful, sometimes it might be useful to at least consider the spirit or intention with which it was given.
So basically what I understand of your situation is that you're living with your mother. When she eventually dies her home will become part of her estate and subject to being divided up among you and your siblings (sorry, I'm unclear if your sister is your only sibling or if there are others). This would mean you would either have to buy out your siblings' interest in the home to continue living there or the house would be sold and the profits split amongst you and your siblings (or however your mother has stipulated in her will). It seems you don't anticipate having the ability to buy out your siblings share in the house so the result would mean that you would have to move. You are in a panic because you don't believe you will be able to afford to live anywhere else. If that part so far is accurate, it seems like you are relying on your mother financially. You've said that she's draining your finances, but if you're living in her home and can't afford other housing then you are also getting a financial benefit from the situation.
You want your mother to sell her current home and help you buy a different home. I'm assuming this is because you don't think you can qualify for a mortgage and purchase the home without your mother's help. This new purchase would be in both yours and your mother's names. Then when she eventually dies, because your name is also on the deed, you get to keep your home and it doesn't become part of your mother's estate...your siblings get no part of it and can't make you move. (Which, honestly, seems like a sneaky, calculated way to keep them from getting part of your mother's estate just because you either feel entitled or you're panicked about your future living situation. Either way it's not exactly fair to your siblings.)
But the person it's the least fair to is your mother. If your mother doesn't want to do this, quit trying to pressure her into it just for your own personal gain. Is there a true benefit for your mother in this plan? Or is it all for your benefit? Because I think I've only really read how it benefits you. Many elderly, understandably, do not want to move away from a home they have lived in for years. Some even decline rapidly once forced into moving. If she doesn't want to move, don't make her. Does it occur to you that maybe the times she has agreed have been mostly because she feels pressured by you and she's trying to avoid upsetting you? The fact that she always changes her mind or drags her feet on taking any steps toward making your plan a reality speaks volumes. It sounds to me like she doesn't want to and you're pressuring her for your own benefit.
It may be time to accept that this "Plan A" of yours isn't going to happen. Maybe it's time to dust yourself off and come up with a "Plan B".