All the emtion aside, you already know that you can't trust her. So, don't trust her.  She stole the money, you know she did it so you and your partner have to now lock up anything of value when she is visiting.  Make it overt, make it obvious and make sure she knows that it is being locked up because she is there.

Grabbing money out of a parent's wallet of purse is not a rare thing for teens to do. Even teens who are trustworthy for the most part.   But, since she is not trustworthy, treat her appropriately.

I have done it myself when I was a teen. But... I always left a note and only did it when mom or dad were not around to ask.  If either of them were available, I asked.  They kept a fund envelope of cash.  So when they were out (they always had their wallet or purse with them) and I needed cash that was where I went.  Otherwise I asked. They usually made sure we had enough pocket cash to have a burger with friends to to catch a movie once we hit our teens.

If BF is accusing you of " Setting up his DD up."  That a major thing.  Hell with his rose colored glasses.  That is total disrespectful to you.  Show you what his real feelings about you are, You are supposed to number number 1. He is supposed to have your back. 
But he putting his POS DD above you.  You can not have a relationship like this.  It's not your fault.  BF is not ready.  He may never be ready 

My SD used to steal from me all the time (I say "used to" not because she gained a conscience and stopped, but because she now lives elsewhere and I don't have to deal with her). 

What I can say about it is that once someone gets into the lying/stealing cycle, they don't just become a good person and stop. It will probably take her getting caught stealing in a store and actually getting into trouble to get her to even entertain the idea of stopping, but most places have such lax punishments for teens (or they think it's "cool" to go to juvie, etc) that this will likely continue into adulthood. I feel bad for having such a pessimistic outlook but in all reality that's what you have to look forward to, especially with little to no support from the bioparents.

I say lock your stuff up (DH and I ended up changing the doorknobs to our room with lock and key style knobs) and installing cameras in all communal living spaces (from reading your post it appears you have some up already which is good) and calling the little thief out on any lies or stealing that you notice, whether her parents like it or not. Also, stop taking her places and doing things for her. Let her mom handle that and if either of them wants to talk sh*t, tell them that you were going to take her, but the money you were going to use for it came up missing so you can't. Petty, I know but if your wife is going to act like $50 isn't that big of a deal, you have every right to be petty. It shouldn't matter if she stole a quarter from you, the fact is that she is stealing.

I have a whole blog post written about SD15 being a thief... My SD is more than likely a sociopath and has zero remorse for anything she does. Yes, I get that teenagers are inherently selfish, but she takes it to a new level with her lies and manipulation.