Since I work with vets, I don't think you will be able to recover anything other than the difference in what the vet told you and the bill you got. Nobody will be able to say the first vet did anything wrong. The bone chips might not have shown up in the first xray,( my daughter always has to have second exrays if a broken bone is suspected, seems they never show up the first time, even if the doctor suspects them too)and the 1st vet did the treatments based on what he diagnosed at the time of the first exam. Things change over the course of two weeks. If an ultrasound was not done on first exam, then he diagnosed what he saw at the time.You agreed to the treatments.When it didn't get better, you chose to have a 2nd opinion.
The second vet did another xray and the chips showed up.. He did an ultrasound and didn't see tendon injuries.(usually ligament/tendon injuries only show up on MRI or CT scan, am surprised an ultrasound showed that, we do ultrasounds all the time and don't diagnose soft tissue injuries) So, he treated the chips. You also chose that treatment .
Now, to be honest, you chose to accept both treatments by both doctors. I know it happens in humans, you go to your family doctor, you choose a treatment based on what the doctor sees. If it doens't help, most folks will choose a second opinion, where the second doctor might see something that did not show up the first time, give a different diagnosis and treat it and all is well.
You will have to pay for the first vets treatments, you accepted them and agreed to them. It is not as if the first vet did harm, the xrays did not show chips right after the injury, sometimes swelling, blood, etc can hide chips and breaks, then they show up after a week or two. Maybe the second vet's xrays equipment was newer and better, who knows.
Now, that said, if the vet kept saying $60 for each treatment then either his bookkeeper did not know the vet agreed to $60 and billed you the regular charge which included the gas and visit, OR like most doctors, human and animal, there is always an office call included no matter what is being done and the vet figured you knew that.
We have folks ask what something costs all the time, we always give the cost of the procedure and then say" the farm call, or office visit is not included in this amount, that will be extra".. When you come in to get vaccinations on your pet, the shots this much, the office call is this much. The only time we do not charge for an office call is for stitch removal. We always charge ranch calls, no matter what the procedure or check up is, and I beleive most vets are the same way.They may divide them between one or more folks at the same place, but the ranch call is always there. Or say, the procedure is x amount and the call in included in this price. Again, knowing vets like I do, he probably said" it is $60" and figured you would know the farm call was not included. I don't know many vets or doctors who do procedures without charging the office/ranch call.
If you go into an emergency room, besides the doctors treatment, it costs so much to just walk in the door. At the doctors office, you may be going in for a return procedure, but you still pay for the office call.
You can possibly talk to the vet himself, not his office manager and explain you thought each visit was $60 including the call when he kept saying $60, and he may reduce it, but there is no way you can expect to not pay for the xrays, etc because he DID do them, whether he saw the chips or not at the exact time of the injury.
A judge might also say" you should have known the ranch/fuel charge are always a part of any treatment, the vet needs to charge for his time and costs, just like any other business.
Truthfully, if the vet is nice and you talk to him nicely, he might reduce the ranch/fuel charge, but in my experience, just because you don't like what the first vet did,and the second vet found something in the xrays the first one didnt, you can't expect to not pay. He did a service to your horse. You chose to find a second opinion when the first one did not help. The first vet did not commit malpractice in any sense, he treated an injury how he saw it should be treated.