do I have any privacy protection if a family member is involved in a civil suit?

No, unless the texts were privileged, i.e. if they werer made to an attorney in the course of legal representation, made to a spouse, etc.  The "expectation of privacy" concept applies to government searches in the course of a criminal case, not private civil litigation, but even if it did, unless the person to whom you texted has a legal obligation to keep your texts confidential, you can have no expectation of privacy in communications you sent to a third party.  Assuming that the texts are relevant to the issues in the employment litigation, your relative will have to produce them.