Single mom dating...

Okay so I should probably start from the beginning... this will probably be long so thank you to anyone who actually replies lol...
Alright so the father of my daughter is not in the picture what so ever no DNA test nothing just believes she can't be his. 
I was a single, party girl that had the mindset to always leave before I was left. I didn't do relationships because I just didn't trust anyone with my heart...all through high school (graduated 2012) till I got pregnant in 2013.  
When I was 7 months pregnant I started talking to a guy( I had talked to him before but it didn't really go anywhere because well "leave before I was left" happened) We talked, hung out. I was still pushing him away like I had done in the past and it was just scary because I was also about to be a new/single mom and not just wanting my daughter to be around someone who wouldn't be in it for the long run... it has been a lot of me pushing and pulling. 
Fast forward to now (3 years later) he's still around. Regardless of how much I have push him away from fear of relationships, the anxiety and depression I have gone through causeing me to not want to see him for months or at all. He has always been there. Still wanting to be a part of mine and my daughters life.
 (Might I add that we have not had sex...I haven't in 3 years and he swears up and down he hasn't either because I'm the only person he wants to be with) 😳 🙈
Within the last month something clicked, couldn't tell you why or how but it's like the anxiety of being with him went away and all I want to do is be with him. 
I am trying to give it a chance because he really is a great guy and honestly I don't think any other guy would stick around for all the curve balls I thrown at this guy. 
So I decided to go with him to his family Christmas again this year(we went 2 years ago) my daughter went with of course. His family treats us like family even though we haven't been around much. BUT now that my daughter is older I don't think she likes him...she has been around him in the past 2 years but not often. The last time she was around him was probably the beginning of this year...
So I guess my question is for the single moms that are dating with little ones...
How was it when you first brought your kid(s) around a new boyfriend? I don't want her to feel uncomfortable and I won't force her to have a relationship with him. She has always been really clingy to me around anyone especially guys. Even family. I have tried talking to her using the word "friend" but it didn't go over well with her. She's 2 almost 3 btw.
I'd love for her to have a male figure in her life she could look up to cause it kills me when she uses "my daddy" in a sentence.. and she says it a lot....she's even called my stepdad "dad"... 😞 I just don't want to force that on either of them. I'm not sure what to do. Will it get better with time? It is definitely new territory for both my daughter and I...