Almost certain you won't have a leg to stand on with this in terms of it being mis-sold and I'm not sure how it will affect your insurance given that it's an existing condition. The fact you knew and brought up the issue of a vet check prior to sale might also be an issue because it shows you were aware this is something that should have been done so you can't plead ignorance (not that being ignorant will help I mean – it just shows you knew the right thing to do and let the buyer talk you out of it)
There are some crafty sods to watch out for and nowhere more than amongst private sellers and auctions. I met a woman with a cob she advertised quite honestly as being a non-ridden companion only and with some minor issues to his front legs as a result of being tethered on a hard concrete surface for most of his life prior to being rescued by her relative.
The relative effectively nicked the pony off the land, brought him home and got him in some sort of half decent nick but he'd since died and this lass was unable to manage him at her place. She didn't want anything for him was offering free to good home but stated he would need to be on land / turnout that was relatively flat or more even than hers which was steep and resulted in the pony being stabled more than she'd like.
Arranged to drive over and meet him and I realised immediately what she meant by her place not being suitable for him to be turned out with the others. Honest to God it was more cliff face than a field so when I got there, I understood what she meant and that it was no exaggeration.
We were looking for a companion and I really took an immediate liking to this cob he was chilled out, laid back and really sweet natured. Brought him out and walked / trotted him along and gave him a good brush and look over and he was in better nick than I'd expected to be honest so I was happy to take him but explained I'd need to have him checked out by a vet in advance for insurance purposes and whatnot.
She suddenly took a dislike to the idea even though I reassured her it was purely for insurance and to make sure he wasn't going to drop dead or had anything over and above what we could manage. I knew he wasn't for riding so she was reassured the vet check was standard basic no frills so he would have suitable insurance cover.
Still wouldn't have it, refused to get back to emails or return calls and texts and just blocked me completely.
What the issue was I don't know because she wasn't selling him so wasn't standing to lose any money, I was perfectly happy to pay for the vet check and to take him on provided the vet didn't discover something that meant he wasn't fit for anything but the knacker's yard and she had land, yard and stables with several other horses attached to her home.
She didn't strike me as someone with any need to dodge the prospect of having a vet rock up and didn't have to pay out or be inconvenienced at all other than to agree to me making plans with the vet to go back. It was bizarre.
Always something massively suss when a seller doesn't want a potential buyer to do the bare ass minimum and you'd think would be reassuring to them.
Really hope you get something worked out and a harsh lesson turns out well in the end for you all.