I don't know if my ex-husband kept stuff I gave him. not really concerned about it either. I have pictures of our daughter and he up on our wall. It's part of my history and who we are.
I know my first love and his mom kept pictures of the two of us and his first wife HATED that. He wouldn't take them down and neither would she - it was part of who he is. it's not like they were prominently displayed or even on the night stand, they were mixed in with other family pictures.
If my ex's house was a shrine to me? I would tell him he needed help. We divorced for a reason....we are better off without each other....while I love the fact that we still get along...no shrine, thanks!!
It's great that you are still friends with your ex. this is great for your daughter!