I have a child like that with a blanket and another one like that with a soother. Ive been able to teach them to put them away. But we have to wait until mom leaves, neither will do it with mom here. The first few times they cried at the door for a few minutes, but now it's like an accomplishment when they put their things away in their bag. They can have them back at nap time.

I think since I made it their idea they were more successful, but they still carry them around at home. The parents can't figure out how I do it.