She's a bit of a full of herself, isn't she?
I totally get that it's heartbreaking when you love someone and have to watch them moving on. Many of us have been there!
But I think she is tormenting herself by trying to pursue the "friendship" with him at this point.
It may be possible in the future.
I see my ex-husband, dd's dad, as one of my top 10 friends now, possibly close to the top 5. We don't socialise as such (he is still with the woman he left me for, so it wouldn't be right on many levels) but I know he has my back and I can turn to him for support in a crisis, advice, share a laugh over text, etc.
But there were many years when we just COULDN'T be like that. Because my heart was breaking.
For her own sake, this woman needs to step away. There may be a time when she can be disinterestedly friendly with him. But that ain't now.
You need to hold the line, OP. You've done brilliantly in making your boundaries compassionate yet clear. No problem with her going to the wedding (why would there be?) but her spending a fun weekend of catch up in your bf's house feels disrespectful to you, and you have made that clear. Rightly so.
See how it plays out. Don't let her drive you away with her wounded lashing out, if he remains respectful and kind and loyal. He's the one you are committing to.
Equally, if he gives any sign that he doesn't wholly favour you over her, I would be gone if I were you.
(Full admission, after my husband and I broke up because he was shagging his current partner, there were certain occasions on which he begged me to come back to him. And on some of those I did entertain it - we even had sex - because I still loved him - despite the fact that I knew he was at that point fully with the woman he had cheated on me with. Not my finest moments, but I do forgive myself. She found out and she stayed with him!
Don't be that woman, OP. If he is genuinely not fully over this ex - if any aspect of his words or behaviour shows you that - don't hang around to be humiliated. )