Your daughter's friend's insurance policy would pay first. Your daughter's policy or your policy (if she does not have her own and lives in your house) would pay second. They can sue you but it is unlikely that you would be responsible for anything if there was adequate insurance coverage.
I suggest discussing this with a licensed claims adjuster and an attorney, if necessary. They will be able to provide you with more details as it relates to the laws in your state.
Many of our insurance company partners have an excellent auto insurance rating and you can get a quote from them here.