You, individually? I'm not sure under what legal theory you, individually, could be liable. If she's a legal adult with a car titled in her own name and insurance in her own name, and her negligence as a driver causes damages, I'm not sure how the injured person could pursue *you*.
Sometimes where members of a household have separate insurances on automobiles, there can be "stacking" where the limits of liability under the insurance policies aggregate or "stack." But that's INSURANCE. That's not you, personally.
Not legal advice as I don't hold Texas licensure. Consult a Texas lawyer if you need legal advice.
As I understand your question, whether you would be liable for injuries caused by her to either herself or another, the answer is no. In some instances, a person may be liable under a negligent entrustment theory for loaning their vehicle to another, for instance when the driver is known to reckless or does not have a license; however, in this case, your daughter is the owner of her vehicle - thus this is not applicable to your question. With respect to her health insurance, she would be liable for anything not covered under the policy and not you, because she is an adult.
I would need more information to understand exactly what you are asking and to better answer your question. If you are concerned whether you will be responsible if you daughter caused an accident and the injured party's medical bills are more than what your daughter's policy limits are, I wouldn't be. Barring any extraordinary facts about the case, I don't believe you can be held accountable in this type of situation.
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