(x-post r/Equestrian) parents are divorcing, trying to figure out if a horse is mine or theirs or both?

The lovely folks at r/Equestrian sent me over here, I'd love to hear what you guys think:

Edit: U.S. resident, over 18 *Edit edit: state is IA

So my parents are getting an ugly and petty divorce, things are being valued and split, you know how it goes. My mom has to buy out his half of the horses, and he has to buy out her half of his stuff. The horse in question is a foal born this year out of my horse. Technically, that baby is in my name since the mother is in my name. I paid for the previous foal's bills and breeding, but it had thousands of dollars in unexpected medical costs at birth so I couldn't afford to re-breed. Since the baby was so nice and my mare is getting on the old side to be having babies, my mom stepped in and paid for the breeding fee, vet foaling bills, and feed for this year's foal. Due to her age and shoddy uterus, this will be the last foal my mare is able to have, so I really want to keep this baby. I've been paying farrier bills and some feed, not to mention that I've spent hundreds of hours caring for all of the horses, training the babies (she has another baby too) for halters and fly masks, feeding, watering, grooming, scheduling vaccines, worming, scheduling and holding for the farrier, and scheduling feed delivery.

So what rights do I have here for ownership of that foal? Is a paid stud fee without a lease just a really generous donation on my mom's part? They used my horse's eggs and body to carry a baby, and the value of the foal is partially due to my horse and her very successful 10 year show career with me. The stud fee alone was $5k, not counting vet bills or any other expenses, so it's not like I can write each of them a little check and be done with it. If it had been negotiated under contract, I would be owed how much selling eggs would cost (no idea on price ???), and using her as a recip mare (about $800 to rent for a year) but obviously there is no written documentation to demand that.

Thanks for reading, I look forward to all of your advice!