Dear L.,
It is very painful for an "ex" to have his child call another man "Daddy" especially when the break-up was not amicable.
My answer as a Mom:
When we became a family, I asked my 8-year-old step-daughter to make up a name for me that felt right to her. I was very aware that her Mom and Dad had an unhappy ending and that her mother would have extreme pain if she were to call me Mom.
Nicky dubbed me Jaina-Mama or sometimes S-Mom. "S" is for "Soul Mom" not "Step-Mom." I explained to her that a Soul Mom is an extra adult who loves you like their own blood child. She liked that.
My answer as a counselor:
1) If your "ex" relationship is not like a Bruce Willis-Demi Moore-Ashton Kutcher relationship...END CONTACT. Do NOT poke at the bear! You couldn't change him when you were married...you can't change him now. You MUST only have a 3rd, neutral-party relate communications. Do "drop offs" only...no "pick ups" for visitation and DO NOT GO UP TO HIS DOOR!
2) It is no longer your business what he says or does...that ended when you divorced. It's horribly hard when he's saying rotten things to your child but, you picked their father and now you are experiencing the consequences of that chioce. Yuk.
3) Realize that you got the cherry on top and the white pickett fence...he's alone (by his own doing...but none-the-less) you can afford to be magnanomous and compassionate. You got the loving husband and the adorable new baby, plus your sweet girl who loves her new step-daddy.
4) Let your daughter know that Mommy needs a little "time out" from hearing about Daddy and that your daughter will be able to talk to a counselor about any issues. I always explain to my child-clients that having a counselor is like having an automatic best-friend who you can tell anything to.
5) Stay OUT of the "Drama Triangles" with your ex. A Drama Traingle is...Victim, Rescuer, Persecuter.
If you are still involved with drama caused by your ex, you never left the old relationship and you are in a 3-way with your new husband and your old one. Yuk. This is extremely unhealthy and is NOT fixable. End contact..did I stress that enough? End contact.
Alright, that's my 2-cents. Good luck my Dear. It's going to take a lot of courage and strong, healthy loving boundaries to turn this big train around...but you can do it! :-)
XXOO, J.