I just want to add that when DU first came out, I had no issue with the ICYA chest, even after moving several times. It's only been recently (since I installed TLS) that the chest isn't working. I switched over to the game I had been playing with DU and both ICYA chests in the house still work fine. I've moved that family twice: once with the ICYA chests in my sim's personal inventory to another house in the same world (Brindleton Bay), then a second time with the chests in the household inventory to another world (San Myshuno). Both moves, both chests worked just fine. Not only could the sim who had originally put the items in the chest access them and move them to her personal inventory, but her daughter could, as well.
When I installed TLS, I started a new game with a new sim. She lived a while in Oasis Springs and collected quite the collection of collectables, which were stored in her ICYA chest when she started university. Now that she's in the dorm, I can only access the items that had been in her personal inventory then placed in the chest (which had also been in her personal inventory) after she moved. She has a cowplant berry in her ICYA chest which has the option to place in world, but she cannot put it in her inventory.
I also noticed after checking just now that her collections have reset. Prior to moving to university, she had completed both the frogs and the eggs, and gotten quite a lot of fish, metals, crystals, fossils, and elements. Now all that her collections window shows is the items that had been in her personal inventory when she moved, which were moved to the ICYA chest then back into her inventory. I noticed that the collections had been reset when I sent my first sim to university in the DU game, but I had assumed that was simply because she had moved out of her family household and created a new one, I had figured that this TLS sim (who had been a household of one already) going to university would just count as moving, and her collections would stay in tact. I don't know if the collections resetting is connected to the ICYA chest not working, I just thought I would share it since I noticed it.
I can share both save files if necessary.