>Here is where I need advice, i told her that I don’t want her being friends with him anymore because I don’t trust him.

So, what you're saying is actually you don't trust your GF. Because if you did, it wouldn't matter if he liked her or not.

It doesn't even seem like she's done anything to warrant you being this concerned, unless you just left it out. You said yourself she hasn't replied to his social media dms/texts (which you knew about), she then set a boundary with him when you asked her to, she asked you if she could go to a party with him (which you agreed to), and then they talked about her boundaries with him... so, aside from hanging out with someone you clearly don't like, what exactly did she do wrong?

>We compromised and she won’t be hanging out with him outside of family things.

...lol this reminds me of the quote "I didn't want a dog, but my wife did. So we compromised and got a dog". You didn't compromise here, you told her how it was going to be, because you're insecure and jealous.