Here's something I want to throw out for someone to ponder, If a person has been divorced for a few years and the one parent that has custody of the two children both being under ten years of age ...
Should? No. There isn't a should here. In fact, I'm not sure you CAN just give up your rights - the state may have something to say about that.
But just because mom doesn't want the kids to see dad doesn't mean dad needs to give up his rights. What he needs to do is go to court and get visiting rights if he wants them. If you are okay with not seeing them, then fine, but you should never have to give up your rights to your children just because someone else decides they don't want you to be with them.
(Exception: The state can sever your rights in the case of abuse if they go to court and a judge decides it's best for the kids.)