If I understand the facts, the correct thing to do would be to take a Voluntary Dismissal without Prejudice against the carrier before the hearing.
Florida has a non-joinder statute which prohibits naming the carrier until a judgment is entered against its insured. Taking the dismissal without prejudice enables you to move to join when and if a judgment is obtained against the insured.
Caution: a second voluntary dismissal acts as an adjudication on the merits and bars another re-file.
Typically, you would sue the driver of the other car.
The other driver's insurance company would provide an attorney to defend them and would attempt to settle the case - and take it to trial if necessary.
If this answer was helpful, please mark it as helpful or as a best answer. This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.
You should consult a local atty to help you on this case. You will likely lose the MSJ and it appears you should take other steps to avoid the hearing. the other side is represented by experienced attys whose job is to blow you and your case out of the water any way possible. That means they will try to trip you up procedurally too. It is hard to acquire the knowledge and expertise to represent oneself in this situation.