@Peamads06,
I am going to operate under the assumption that this is a lesbian relationship. Note: this is not strictly a gay forum so most people would not know WTF was going on without an assumption such as this.
Questions for you:
You say you have been together for a year and a half. Did she cheat during your relationship, or just before it? Because if it was just before, and not during your relationship, I would say that the Statute of Limitations has passed on this being a big issue.
Yes, this is an ex, and it's a jealous ex. But does your girlfriend show any inclination toward wanting to be with this ex?
You say things haven't been great between you and your girlfriend. That's a different issue, okay? Perhaps counseling would help you both to get to the root of your issues.
Your pronouns are a little hard to follow here. I am going to assume another thing, that your girlfriend has offered for her ex to stay at your (you and your girlfriend's) house. Is that correct? Then it is
your home, for gosh sake's. If you can't trust your girlfriend to be faithful under the roof she shares with you, then it's all over but the shouting.
BTW, flirting while drunk? Hell, I am the biggest flirt I know and I have been married for almost a quarter of a century. I flirt drunk or sober; it's immaterial to me. I also don't act on any of it.
Flirting is not the issue.