My sks are grown now. While their mother bought most of their clothes we did have a few guidelines/rules.
1. Things that got left there didn't get fetched (at least a 2 hour trip) til the next visit. Same for the reverse. If they went to Mom's without a swimsuit, they had to make do. They saw her EOWE, holidays and summers. This was the biggest one and the one that IMO taught them to be responsible. Stinks to not have shoes to play in or a jacket you want to wear.
2. They kept some basics at both houses. A pair of shoes. Some jeans and shirts. Underwear. Even if they forgot to pack, they had something.
3. Some people do labels. Mabel's Labels has some great tags and you can put them in your stuff. You can also use different colors so the kid has the same name but knows that Mom's house is green and Dad's house is yellow. They last a LONG time. Teach her to bring back the green ones to your home.
4. When SD was little, she brought another backpack to before/after care. She was able to leave it with them or leave it in her classroom til aftercare. It wasn't always feasible so sometimes we had to leave a bag somewhere for her mom or her mom had to come by only when we were home til SD earned a house key. Talk to the teacher about being able to store a bag. Maybe the office would hold it? Have a travel bag so she has a place to put her shoes and headbands when she takes them off. You might also ask the teacher/school to reiterate what is appropriate to wear to school. SD's school sent us a note about clogs when they were popular. DD's school J. sent a notice about weather wear. You might simply quote the school handbook and say, "Ex, can you make sure Emmy has the right shoes for play? I know she loves her fancy shoes, but they're not allowed in gym class." Or "I had to talk to Emmy because the teacher said she can't wear open toed shoes at recess. Can you help reinforce that from your house?" In our case, the clogs had to become "sometimes shoes" because the school didn't like them. We hated them, too, but had allowed them because her mom got them and she loved them, but once the school said it, they were done.
5. If your ex is remotely reasonable, ask him to pack the shoes or headband or whatever so that some come back. I would not buy more. I would tell her she needs to bring them back or she doesn't get to wear them or sleep with that bear or whatever. Really young kids need help. It is in their best interest if we can all be adult about it and J. pack the stuff when the kid needs it.
My cousin's mom never allowed anything to go from house to house so she had all these pristine toys she never used at her mom's. While I get that it's hard when you paid for it, most of the time we let the kids take what they wanted. It was theirs. It was their responsibility J. the same as if they took it to school or to a friend's house. Some tough lessons were learned, but they made it through. Otherwise SD would have a Wii she barely used or SS wouldn't have his alarm clock over the summer because it was an iHome I bought.