Op you may not mean to. But you come across as the family members who turn up, after not doing anything the criticise the care their elderly relative has. But doesn’t do anything to help. Just criticise.
You hint your mother could be quite toxic. The fact that she wanted a 2 bed place building, doesn’t mean it was possible. Since you seem to reluctant to actually have a conversation with your sister, I am guessing you don’t know the details.
Your sister and her husband, if they are so clued up to attempt to deprive your mother, will know that putting her in a home (if it’s at all possible) will, potentially, cause them a financial problem. But they still think it’s the best thing.
Since you haven’t been the one caring for your mum, you have no clue the impact she is having. or why they are doing things the way they are. It may come across as controlling, but likely they are just trying to do things in a way that causes less stress. I remember grandad, causing all sorts of problems when he had spoke to someone on the phone. Because he would out and out lie about the conversation. He would lie to other people. He once told neighbours he woke up to my cousin sneaking around his bedroom stealing from him. She wasn’t, she was at my house. So yes, we didn’t really want him talking to people without someone there. Because in this instance the neighbour called the police. Grandad was toxic. He loved causing issues. Between the family and others or within the family. He was always the same. He loved winding his eldest daughter up on Christmas Day until she would snap. Which is why we stopped spending Christmas as a family.
Looking after him was exhausting. It aged my mum terribly and she died less than 6 years after him.
You seem full of reasons why you couldn’t do anything. You didn’t see the plans, you don’t know the detail, you weren’t there for this happening or that happening. But you also seem to have a really solid opinion on what’s happening. Despite not actually being around for any of it.