How would you handle this?

Actually Have been in this situation and ended badly for me. So No you are not wrong and emotions can screw up even the most trustworthy of people. They are not perfect and it is a hard thing to tackle. So you are totally in the right for feeling that way and she really should take a hint and not meet this guy alone. Meet with him open place with people around say your goodbyes and rip the bandaid off and start your future if not as mean as this is to say she does not have your feelings in her mind just hers and that could lead to worse problems down the line.

I would PROBABLY let her see him, it's really hard to get over someone(friend or ex) so I kinda understand how she feels

This is actually very tough, because one you might seem like super possessive type if you tell her to stay away and what not and secondly I feel like she doesn't know what she wants. I was at this point once, my experience was that I told my feelings and that she is a bird I'm letting go to find what she wants in this world but I will leave the window open hoping very strongly that the place she flies to is back to me. For me she never came back but I believed she would we just have to hope and trust.

Accept that she's going to do what's best for her, and that you are going to feel what you feel. Go ahead and look into a family therapist to help you through this. This is one of those situations where an impartial third person hearing both sides can work wonders.

I'm going to be real straight and say either stop her or just break up with her because she's going to screw you over. I've seen this scene play out A LOT and every single one of them for the bad. A girl who is not over their EX and is still confused is a girl who is using you as a rebound. The moment they are over their EX and you've helped them by getting them back on their feet, they'll leave you for someone they think is more fit. Completely blinded by the potential you have for them. Yeah sure, I sound like a jerkstore but I'd leave her in a heartbeat, obviously it's a lot easier said than done but either you stop her or you let her go and break your heart. It's your call.