Look, moldableman, you are not the first man to step in and parent someone else's child. You are not the first man to marry a women that deeply regrets having had any sort of relationship -- much less a sexual one that produced a child -- with a man she now considers a loser and she shudders at even the sight of the man or the sound of his voice.
You need to hear this clearly ---
It is not a contest.
It doesn't matter what you think of him.
It actually doesn't even matter with regard to WHO the child should legally be calling "Dad" if "Dad" does end up being an abuser EVEN IF he were to be convicted of the same (which I realize hasn't happened, abuse allegations have not even been substantiated).
I'm just making it very clear that none of these are grounds to NOT call Dad "Dad" and/or to call ANOTHER man "Dad". Period. End of story. Even if.
I am both a stepmother and have remarried with children from a prior marriage. I'm not going to go into detail for the sake of this discussion, but your situation is not at all unique and you need to stop acting like it is an using emotional arguments for legal questions. Period. Even if.
Now, on to the "harassment" situation. There are many ways to curtail conversations to just the basic minimum. I mentioned that I am remarried. My husband has children and therefore an ex. She is a nightmare and she always will be. That's just the way she is. For the most part, there's nothing my DH can do about her poor choices. And, that is EVEN THOUGH they have the standard verbiage in their court order not to disparage the other parent, etc. Of course she does that.
My husband keeps as much of their conversations to email as possible. She tends to fly off the handle, be impulsive, immature, etc. At least by having to stop and write, she can think a LITTLE (apparently not much) about what she says. And, so can DH because she's awfully maddening.
When he's said all that he needs to, he ignores. When she calls his cell phone, the house phone, rinse, repeat, etc., he ignores. For the most part, he talks to her very rarely "live". At times, he will when the situation is tame enough because her ego loves the attention so when it's "safe" for him, he'll feed it a little. Also if he knows he HAS to take a call from her b/c of something going on, first thing he usually says is "I only have a minute, what do you need".
You just have to let your wife put her big girl panties on, so to speak, and manage her relationship with her ex. They once did all that, talking, etc. including having sex to make a baby so not to be crude, but she didn't need someone there protecting her then so give her more credit to deal with him, just encourage her to (a) read the posts written here that are for HER vs. having the information come through you and (b) encourage her to disengage from convos that are going off track and not producing anything worthwhile. And, FYI, there are ways to do that without adding fuel to the fire or being as immature and impulsive as the other party. She can warn him that the conversation needs to be about XYZ and that she will need to end the call if it goes off track. Then if it does, she needs to follow through.