I have had to file motion for enforcement against my ex-wife in order to see my daughter. This year it took 5 months for the judge to finally hear the case, because she was awarded a court appointed attorney and then fired him and hired her own who she failed to pay. The courts continued to show favor on my ex-wife even after her attorney with drew due to her non-conpliance.
Because of the witness and video proof of her vilating my visitation she hired a attorney. I cannot afford an attorney so I have been representing myself. Due to my limited experience I lost my case when her attorney was able to find favor with the judge. Her attorney also filed a countersuit: motion for enforcement of back child support, motion for sole custody, and motion for increase for child support. I established back child support when I went to mediation with my ex-wife during the second part of our divorce.
Originally I had primary custody of my daughter and my ex-wife was ordered to pay child support. She took me back to court when I remarried and the same jude re-opened my divorce while married to my current wife and to end the fighting I settled on mediation and allowing my ex-wife to have primary custody with extended visitation for myself and set child support not to be increased for 3 years.
Long story short, I have had to fight for this visitation since it was granted. The judge went back and instead of making her pay the child support owed to me, he charged arrears against me dating back to the date I filed for divorce. I have been working and going to school and only able to pay small amounts consitantly each month since the close of the second trail. I have proof of making payments each month and the attorney general reflects the same record.
I went to pick my daughter for my weekend visitation today and was served. I am tired of fighting in the courts for rights to be a father to my daughter. I have been a responsible and dedicated father since my child was born. This constant battle from my ex-wife is affecting my daughter and my marriage.
Since my ex-wife wants to take away my rights and not allow me to see my daughter because I am remarried, then how can I petition to the courts to reliquish my both my legal and financial right to my daughter.
I have never relied on child support to take care of my daughter. I pay child support and I provide for my daughter. However, if my ex-wife wants me out of my daughter's life then I should not be obligated to continue to pay for my daughter if I have not access or involvement in her life!
I have to continually petition the courts on my own just to see my daughter and even when I provide proof of her not allowing me access, the courts provide no assistance or consequence to my ex-wife when she violates the court orders continuouslly.
I am so tired, hurt, frustrated, saddened, and willing to place my daughter in God's hands.
All I do now is pray for my ex-wife and pray each time I go to see my daughter, God will allow me to see her.
Any suggestions?

No you can not just give up any rights.

Your problem is no attorney,

What a sad situation.
From what I understand one is required to pay child support whether the custodial parent allows visitation--they are separate issues.
Your ex-wife is setting up your daughter to resent her in the future by not allowing you to have a relationship with her. I speak from experience--I've never met my father and I blame my mother.
If you give up your parental rights though--then you are setting up your daughter for possible future self esteem "issues".. that you didn't want her or care enough to fight for her. Besides that, you have a moral obligation to provide for her no matter how her mother behaves. At least you will know you have done the RIGHT thing in supporting her at least financially--if that is only the extent you are allowed at this point.
Don't give up on your daughter. You may have to wait a long time for the reward--but it will come. You have God given rights to be a father to your child. Your ex is making your daughter be fatherless--when she doesn't have to be and I don't believe God looks kindly upon that.
Ask Him for strength and wisdom on how to handle this... and please don't give up on her.

You cannot give up your rights, only a court can terminate parental rights. And courts are very reluctant to do so. Generally they will only do so to clear the way for adoption or if the parent represents a danger to the child. And they will not do so to allow a parent to get out of paying support.

I know you think you cannot afford an attorney, but you cannot afford to not have one. You've seen what happens when you go up against an attorney on your own.

So, the bottom line is that you can't give up your rights and you can't get out of paying support unless you can regain primary custody. So you are better off fighting then laying down.

How old is your daughter?

What a sad situation.

If you give up your parental rights though--.

Yes this is a sad situation. But this is the Family LAW forum. Reponses to this forum need to deal with statutory law, not emotion or relationships. Your response included two points in reference to the law. One correct, the other incorrect. Yes, support is separate from visitation. But a parent can't give up their rights.

But the rest of your post, while good advice, was mostly inappropriate for this forum. You are new here so you may not be familiar with the way we do things, so this is just a friendly note for the future.

What state is this in ? It sounds like your not filing the proper paperwork and its causing your case to bog down. There are other ways to deal with this situation and to ensure that you get your daughter.

What does your paperwork say about your current visitation. Also Im not sure your understanding the law but once your divorce case is closed it can not be reopened. So Im not sure what's going on there.