It's likely not your gym you'd be dealing with but rather their insurance co and possibly the company that did the repair. I'd bet they both point the fingers at each other. In this case a lawyer could help.
It sounds as if you have an attorney because your deposition is set. I would suggest you express your concerns to your lawyer if you have one. I am sure they will "prep" you for the deposition and that will alleviate your concerns. It is standard to do a deposition which is simply a question and answer session under oath. Your attorney will tell you the guidelines and to tell the truth. good luck.
The money is in trust because the lawyer is likely negotiating with the hospital and doctors to lower the bills. Once he or she gets those lowered you will get the remainder. Call you lawyer and ask if he/she is negotiating the bills for you.
Lots of questions here. Parents can be sued for negligent entrustment so in theory the at fault driver can be sued, possibly the parents, etc. there may be multiple levels on insurance coverage and there may be under insured coverage. Need more details here. If the insurance is not enough then one can try to go after assets. Hopefully this answered it for you but if not, reach back out. Much will depend on how serious the injury was.
This answer is general information and not intended to create an attorney client relationship.
You can terminate an attorney client relationship at any time via telephone, email or letter. My suggestion would be to express your concerns directly to that lawyer to see if the relationship can be salvaged. We can't fix what we don't know about. If that were to fail then you can terminate as indicated above.
Under South Carolina law yes Most take it if they have to "fight" to get it or it was a denied case and then now it is accepted and you are owed back TTD. That is money secured by the lawyer that the insurance carrier had otherwise denied.
I've seen this before. Horseplay must be mutual. That is an employee push. She should get an experienced SC workers comp lawyer. Check ratings, reviews and take advantage of a free consult. Only thing you need to make sure of is that your daughter wasn't also engaged in horseplay. Let me know if you have other questions.