That is not what posters are writing.
Your daughter has gone to live with her dad - that is not a punishable act. Moving home doesn't mean that you can't have personal trinkets that were gifted to you.
Teenager girl has another home to move to when the teenager years get tough, with mum doing the parenting.
Unfortunately you are in a situation where instead of dad bringing her straight back and saying "lets parent together" he has allowed this to happen.
Your daughters belonging though are hers, and saying that her being Abe to have her belongings would be rewarding her "bad" behaviour is not correct. You would be manipulating and controlling to withhold someones belongings
It's really a gut punch when a teen moves out because they don't like your rues, then moves to your ex house. The silent treatment from a teen is also hurtful
Instead of trying to manipulate the course of events
Stand back, be pleasant. Show your daughter how an adult behaves. Text her and say of course she can have her trinkets etc. You may be angry now, but the door is always open when you want to talk.
I can assure you things will be honey moon stage at her dads right now, but give it 6 weeks of the school holidays and it will be carnage, he may try to keep this secret, she will not say anything - but it will come out in the end. It will be a nightmare.
Make sure your daughter knows you are there for her when she does need you
Make sure you don't manipulate the situation
Make sure you don't take this entire situation personally