If a tire or repair shop does negligent (careless) work in some way, they are potentially liable for any/all costs and damages directly caused by their negligence, such as the cost to repair a car, replace a tire, towing, etc. If they will not voluntarily provide such compensation as you find acceptable (e.g. a refund), your recourse would be to sue them (potentially in small claims court, where you could act as your own attorney) and prove by a "preponerance of the evidence" (more likely than not) that they were negligent and caused the tire to fall off.