@sylvie I'm sorry this happened to your daughter, OP
Getting cheated on hurts horribly.
I read that she was considering going on a trip with him as friends. How long has it been since the breakup, and when exactly will they be going? I honestly recommend you trying to convince her otherwise. Going on a trip with someone who cheated on you, and someone the family once considered a son, might make it way harder for your daughter. I don't know what type of a person he is, but if he's moved on by the time they've gone on the trip, certain actions he does might have negative reprecussions on your daughter's mental health.
When I got cheated on and dumped, both my parents helped me by comforting me and making sure I stayed as far away as possible from my ex. While they didn't try controlling how often I texted him, they constantly took it upon themselves to remind me that he didn't deserve my kindness, because that was me "letting him off easy." I wish I listened, but instead I kept in contact with him until he moved on and disrespected me so much until I had enough and cut him out of my life.
Regardless on whether her ex is "mature" or not with how he's handling the breakup, I still would advise that you try your best to convince your daughter to cut him off and focus on healing. She deserves it.