Inconsistent father and torn mother...

Hi guys. A little about my family. I found out my BD was cheating when I was 4 months pregnant with my daughter. I tried to make it work and he wasn't interested. He wouldn't even put himself on my daughters birth certificate because he wasnt sure she was his (I don't understand why he even said this) I started hanging out with my now fiance when I was 7 months pregnant (just as a supporting friend I'd known for 6 years). I gave birth to my daughter and my fiance has been there ever since. (2 years now) She calls him dad and he is a wonderful father. We now have a newborn son as well.

Her biological father has never wanted a parenting plan (I have suggested we get on one multiple times) and has never paid child support. He doesn't buy her things very often either. Her birthday was recently. We invited him to the party and he came. He kept making inappropriate comments to me about me and my mom and twin sister (they are really beautiful). I had to explain that those are his daughters auntie and gma even tho me and him aren't together.... He did not buy our daughter a gift. He sees her a few times a month but would just come to our home and hang out. We are no longer comfortable with him being here as its just awkward. He said "Roger that" when I explained that from now on he could pick her up after work I can pick her up from his house. Its been almost 3 weeks and he hasn't visited her. She told me she missed him cuz she saw a picture of him so I sent a video of her telling him she loves and misses him.... he said he would try to come see her soon. Today he texted me asking if I knew of a place for rent and then said he's been busy and he would try to see her up soon...

I guess what I'm trying to decide is if I should even let this inconsistent behavior continue...it breaks my heart that he hardly makes any effort. I don't want to keep them apart but I don't know if this is negatively affecting her...?? my fiance wants to adopt her because he will always be her dad in his eyes even if we split. So she will always have a father regardless. Ugh mostly venting I have always worried about this her whole life and i am just looking for some outside perspective.