Why are you making this so complicated? Just drop your end of the fight. Don’t set her up to steal from you by having her anywhere near things worth stealing. Don’t respond to provocations. You can’t change her. You can’t make her love your guy as much as she loves his brother. You can’t make someone who is an addict and behaves like one want to clean up her act.
Talking, reasoning, screaming, and cajoling won’t work. You can’t reason someone out of unreasonable thinking. If she tries to pick a fight, all you need to say is something like, “I’m sorry you feel that way. I don’t agree so let’s move on.” If she persists, simply, quietly and calmly leave! Don’t give in to the temptation to start a fight by moralizing, preaching, begging her to be nice or scolding her. As you’ve pointed out, it discourages you both even further.
It’s the relationship with your fiance that is your first consideration. If he can’t back you up in staying out of the fights, you have another problem. I hope he learned long ago what I’m trying to tell you. It’s up to his mother to decide to change. He can’t do it for her. You can’t succeed any more than he can. Hopefully at some point she’ll understand that she is losing the chance to have a wonderful relationship with her son and new daughter-in-law and will get herself into treatment. Until that time comes, all you can do is lovingly and calmly detach from the whole thing.
I wish you well.