First of all, they should be paying you for making their horse a better horse. you are essentially "training" it. They should be darn grateful to have a lessee like yourself. They don't come along every day. They could have their mare in such worse hands!
maybe talk to them that you want to take care of the shoeing yourself. renogotiate the fee to exclude hoof care, then you can do it on your own.
As for the bucking, if the horse won't lift one foot (the rear?) it could mean her pelvis/back area is out in some way, as lifting that last foot means bearing weight, perhaps, on the bad area. Maybe spring for a chiro visit.
I could not deal with a hrose that is bucking, just as most average riders cannot. They will have a hard time leasing her to anyone else if she is a bucker. I think you have grounds to renogotiate some of the fees.
I really don't have much advice on the bucking issure, sorry.