As a daughter of divorced parents I'll say this.
It is much better to have your parents divorce than living in a unhealthy family, that said it is extremely important that you keep your kid totally separated from your problems with your ex.
If you are in a situation were you can get professional help that would help you and your kid tons if not this are things that I can tell you.
My mother always used my sister and me to get to my father, to ask him for things or as messangers.... that made an extremely difficutl relationship with my father and now that we are grownups I know she did wrong... very wrong.... we were just little kids and shouldn't have been in the middle.
Now my father is dead and you can see, feel still the hate and resentment my mother has towards him and now that he is not here she doesn't know where to direct those feelings and she is taking it out on me that I was close to my father... (as close as possible given the circumstances)
My parents separated when I was 3 and my sister 5. Thirty years later they could still not be in good/respectful terms.
I would think this..... try to have as much as a completely civilized/respectful relationship with him. If you can get over him completely and you can even be sort of friends for your baby's sake that would be even much much better.
Make sure you are ok first.... make sure you get over your problems and over him. Get emotionally healthy that is the best way. I think my mother's main problem is that she never worked on her and she never got over all the problems with my father soooo she became bitter towards him and all men.
As setting your boundaries, if you two can do it by yourselves good. Sit down with a peace flag and talk about YOUR KID AND HOW THINGS SHOULD BE MANAGED WITH HER.
Not using your baby to bother, get to him, compete or anything else. Try to keep your head as cold as possible when the relationship of your baby with either parent is concerned.
Know that if you try to hurt and spot the relationship between her father or the other way around, him trying to hurt the little girl relationship with you will MAINLY AND MOSTLY hurt your kid..... and sooner or later will backfire. (that is just a little warning... IT DOES BACKFIRE)
At the same time, talk as honestly as possible in an appropiate language and manner to your girl. Do not explain the main or real reasons of your separation if that is something that will damage anyones image, but make sure to let her know that she is NOT responsible and that she still has both parents and their love for her is not going to change.
Do not let /allow the play that if you don't get me this my dad will, or viceverse, have as much as possible open comunication with your ex so you are in the same page as educating your kid. Set the same boundaries and standards and respect each other's authority.
Be very very careful as not letting anyone else talk bad of you from his family or anyone in your family talking bad about your ex... at least nowhere close to your kid.
Know that each parent IS important to the kid, and having a healthy relationship with each one will help her grow up happy. Some times that is not possible because the fathers are not active or present in the kid life and that would be out of your hands but do not be you the one creating that sad escenario.
I love my mom, and I know she did her best but I can not help think that my life would have been much much more easy and with much less tears in the way if she had gotten over everything, faced her pain and problems and worked on herself to be ok and move on. And ofcousre if she had been more aware of the things that you should never do to your kids in relationship to your ex partner..
I hope this helps. When I see this kind of questions I can not help to think about me and my parents. I know that every situation is different but I do know something works for every and anyone..... GET WELL YOURSELF FIRST.... BE PRESENT AND LOVING.... BE AWARE AND CONSCIOUS OF WHAT IS REALLY AND HONESTLY GOOD FOR YOU AND FOR YOUR BABY...A lot of times what when in doubt it helps to try to see things from the shoes of the person you have the question about.... in this case your girl... what may she be feeling, if it were you what would you like it to be.... what is the best for her and for you.... as always don't do unto other what you would not like for you and you will get a lot of answers there as how to manage the situation with your little girl.
I am so sorry you are going thru this. Know that life is so beautiful and the pain and bad times WILL pass.
You are so brave!