Can the Insurance Company Sue
When a person fails to fails to uphold a duty of care and that lack of care is the cause of foreseeable harm to another, that person may be found liable for damages due to negligence. Negligence claims require the plaintiff to show the defendant owed a duty of care, that duty was not upheld, and that failure of care caused a foreseeable harm. A failure to obtain required licensing won't prevent a person from being liable and will often be used to prove that applicable standards weren't followed, and therefore the duty of care wasn't upheld.
In negligence cases, the most difficult issue to prove is often causation. In cases of auto damage, expert testimony of mechanics and others may be used to prove the cause of the damage. It would need to be shown that the damage was the result of the defendant's actions or lack of care, and that there were not other causes or contributing factors which would entirely or partly relieve the defendant of liability.
It is possible that the insurer will file a negligence claim against you if your daughter submits a claim. It will be a matter of subjective determination for the court whether there was negligence, based on all the facts and evidence in your situation. Some of the factors, among others the court may consider include what the weather and driving conditions were, whether there was previous transmission trouble, and the method used in towing, and standards for towing by towers in your area.