It will be difficult to prove the park’s liability for this type of injury. It sounds as though your husband knew about his bad back before going on the ride. If the ride had some type of sign posted, or an employee made an announcement, stating that people with particular medical conditions, including back pain, should not go on the ride, your husband will be deemed to have accepted that risk in deciding to go on the ride. Even if your husband didn’t see the sign or the ride didn’t have such a sign posted, the park will have a strong argument that, as a back pain sufferer under a doctor’s care, your husband should have known that the bumper car ride might aggravate his back condition.
You need to talk to an attorney who is experienced with these types of cases to give you an honest assessment of your chances of recovery. Your attorney may be able to structure a case, depending in particular on what notices were posted or announced, that will allow you to receive some type of settlement from the park.