I’m not a lawyer, but I do think this is worth pursuing through small claims court. You may well have already talked to your SIL-lawyer who may have given you an opinion about the worthiness of this claim.
While I think it’s worth pursuing, I also suspect that your leasee has money problems. If nothing else, it sounds as though she has a pretty serious cash flow problem. She “lost” her credit card doesn’t sound remotely credible to me, except in an extremely literal sense of “the credit card company cancelled my credit card because of non-payment.” The fact that the lessee initially said she would pay the vet bills and then apparently withdrew that offer (probably when she found out how much they would be) also suggests to me that she has money problems.
If that’s true, even if you do get a judgment in your favor, getting the money may well be a different story.
Just on the issue of proving that the horse’s colic resulted from not getting the supplements: CrowneDragon made the point that I wanted to make. It may not matter whether you can prove that; what you can prove is that by not continuing the supplements, the lessee effectively made it impossible for your horse to be covered in case of a severe colic. The big issue here is that you’ll need a fairly savvy judge who will understand why that could potentially be a big deal and is a real harm done to you.
And just to note that not all free leasers are terrible, the horse that I now own and have owned for 13 years I originally took on a free lease for 6 months.
Good luck.