| Is this just you talking or is it your husband? Do you want his rights terminated so that you do not have to develop a workable relationship with his child and that child's mother?
It sounds more like you wanting this to get rid of what you perceive to be a problem and threat to your marriage. Your husband had an affair and a daughter was born. Bet that just burns you up - and it would be a reasonable feeling. But you need to rise above that and deal with what is really in front of you. Your own feelings of insecurity, resentment towards your husband and his affair, and the child, that he will be supporting for many years to come, as well as your behavior of stalking.
If you have gone to counseling, please get yourself there. This situation is very stressful. Without knowing the "other side" of this situation - it would be interesting to read what your husband feels and what the "other woman" has to say. - it is difficult to say what is best. If you continue to act in the ways you have towards this woman and child, you will find yourself in some legal trouble.
Would the child and her mother be better off without the presence of your husband in their lives? I do not know. I am not condoning the affair he had. I think men that cheat on their spouse are no better than slime. But I also know that there can be redemption and forgiveness and the marriage can survive. Actually become stronger.
But you need to get a grip on your own emotions and actions. Please seek some counseling - if you do not wish to seek a secular counselor, then talk to your pastor. Hopefully your husband will do the same. About his daughter - she is innocent and should be given all consideration in any decision. One cannot wipe out parenthood just by signing a paper. | 
I am confused
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