My mom is always making negative comments about everything and everyone. How can I address it?

Some people are just that way. Since, it's unlikely that she will change, I'd try to just accept it. If it's too intense, let sister address it, if that's where she lives. You might mention it to her doctor, to rule out depression.

Maybe sister should say if she is so unhappy there she will find a nice AL (if Mom can afford it) or a nice nursing home. If Mom can still do for herself maybe an independent living community, If thats not what Mom wants then she has to stop making everyone miserable or thats what is going to happen. Your sister needs to set boundries. Its sisters house that she has allowed Mom to come live in. She is not to defy her authority with her kids.

Mom will do this as long as its allowed.

Mine does that too - I was just talking about that with some friends. Basically, my mom has never really been happy that I can tell. She married 3 times and didn't like living with any of her husbands. She didn't like living alone, didn't like living with me and didn't want to move in with any of my siblings. Now she is in a dementia care facility and - surprise! - doesn't like that either. She calls almost every night to tell me her gripe of the day. (I confess, sometimes I don't answer the phone.) She was taken aback when - exasperated - I asked where on earth she actually WOULD be happy. "I don't ALWAYS complain," she answered. I assured her that she did and that her negativity might be one of the reasons that family and friends stayed away in droves. I urged her to just try not to complain to the first visitor that walked in her door, try to find a cheerful topic to talk about, or take an interest in the person visiting by asking THEM about their day and their interests. She is a little better about it now - I think she did actually understand that people find such negativity off putting after it was pointed out to her.