I don't want to be with my baby's dad no more and I had no place to go so I am staying with my grandmother to get on my feet so I can provide a me and my daughter with a house with me but in the mean to I have my daughter with the father so she has a nice place to stay just until I get my house but everyone is telling me that I am abandoning my daughter and that I have to stay with the father of the baby but I don't want to be in an abusive relationship I don't know what to do anymore I need help?

It is not so much that you are abandoning her as that the court will look at it like dads is where she is accustomed to and he could turn around and fight for full or primary custody.
Why can't she live with you and you go after him for child support?
Have you at least gone for court ordered visitation's so that you have some standing that he can not say you are neglecting her? With just seeing her when you can doesn't look as good to the court as having visitations where you take her for the weekends or whatever the court order says.

If its an abusive relationship.. why would you leave your child with the person making it abusive?

How if it only fair for you to leave... and not the child?

Sometimes guys are abusive to the mother and not the child
BUT I would be worried too.

Sorry to hear that your going through this, as far as custody is concerned if you can, try to get someone else to take her into there home or wherever you are staying because if you feel that she is better off with you than that is where she should be at all times. Until, you get your own place, do your best with what you have!! Your bond with your child will only grow stronger but by all means, if she is better off with the father in "your eyes" at the presant moment then let her be, things have a way of working themselves out.
Then-make no excuses be true to yourself and your child at all times. Stay clean and sober if that was ever an issue. Stay positive with a strong attitude, God Bless!

Yes, since you did not take the child, when you latter try to file for cutoday the father will have a much better chance of winning, since you left the child there, and since he has proven he can care for the child.

If the father of the baby is abusive, why would you leave the baby with him? Even if you only know of him being abusive to you and you don't "think" he'd hurt the baby. It doesn't sound like a safe situation. The Judge will probably see it that way too. If you felt like you had to leave for your safety you should be taking the baby with you. If the father wants custody of the baby he will get it if you leave it there with the father.