Should I Stay or Should I Go?

Exactly how did she almost break you up?  Did she come on strong to him, flirt with him, have sex with him?

"I don't necessarily think it's a trust issue or that we aren't over the problems from the past, but rather a practicality of being proactive and not placing ourselves in such an awkward and uncomfortable situation. "

Yes it is a trust issue, and if you don't trust each other 100% then you should not be together and most importantly NOT move in together.  It doesn't sound like you have not overcame the issue yet. 

You state she almost broke you up......she didn't do this really, she wasn't the one you were in a relationship with....He was.  He is the only one that controls his actions, if he let it get to a point of almost breaking you up, that was his choice.

" It's also the only neighborhood that we can afford that is in the school district his daughter wants to be in so I feel like I am stuck.  What am I supposed to do?  "

You can choose to leave or get counseling to work through this issue.  Usually when trust is broken because of infidelity it takes professional counseling to work through and build the trust back where it needs to be.

Yes please explain what issue you have with her other than your BF went to high school with her???????

If your BF wants to cheat with her or anyone else, he can do that without having to live in the same neighborhood as the other woman. Living in the same neighborhood as another woman does not guarantee he will cheat and not living there does not guarantee he will not cheat.