I have an exwife who is doing everything she can to make my new family life very difficult. I ask this question only as a last resort. How do I and can I relinquish my parental rights?

Your ex is being difficult so you want to discard your kid(s)?

What a stand up guy you are.

You cant, unless your ex has remarried and she and her new husband want to pursue a step parent adoption. IF (and they wont) a court were to issue a TPR order it wouldn't change anything except take your rights away anyway - you would still owe support and your ex would still be able to make your life difficult.