Give yourself time... one thing that I have learned is not to rush into anything. I have some questions:
1) You did not list what your problem is, are you trying to figure out which one to get with or date? The answer would be neither, give yourself 6 months - 1 year to be relationship and drama free for the sake of your daughter.
2) Is the father of your child paying child support? If no, the only thing ya'll need to talk or think about is finances and him paying the support. If yes, work out a visitation agreement with your daughter.
3) With your Friend/Stand in Father figure ask yourself long term do you want to be with him? If no, then take the appropriate steps and be free of relationships for a while to just be with your daughter and work on yourself.
You mentioned you were young, I don't know how young but in general the younger you are, love usually goes back and forth but as you mature you will realize that love does not require a lot of drama. Your child's father has not taken responsibility as you mentioned so he wont make a good long term mate. Your mother don't like the stand in father figure due to the past, he is not worth the drama being caused between you and your mother. There are plenty of great men out there and you have a daughter involved choose wisely because these are the men she will look up to and base her foundation of what a man is suppose to be. I know from personal experience because I have a 5 year old and I am the one who selected her parents. As women we have to choose the right man for our children so they will succeed in a messed up world.
ETA: Break up to make up is not reality for most couples. Choose a man who will be a man and wont walk in and out of your daughters life.