@Mrsmarple2002,
I don't know what you mean by domestic abuse, do you mean physical violence? If so, you should have no problem getting a protection order. If not,
you should work together with the father for the good of your son.
When I went through this process, my ex and I started fighting legally. We then decided to stop fighting for the good of our daughter. We negotiated a custody arrangement that included a strictly worded parenting plan.
I got Monday and Tuesday. She got Wednesday and Thursday and we alternated weekends (Friday - Sunday). The plan specified each holiday (I get Thanksgiving, she gets Christmas). The plan also has some other things that are important to one of us or the other (i.e. travel, and a prohibition on corporal punishment).
Funny thing.... after all the fighting and a little time had passed, we realized that
it is easier to work together than to fight. My ex-wife would have a workshop on a weekend when she had my daughter. I said "no problem". Then I had a conference I wanted to go to and she said "no problem". Let me tell you, being single with a child is not so easy.
Having a good relationship with the father of your kid will make things easier for both of you.
Of course the real benefit to cooperating is to the child... no child wants to have parents who are fighting with each other.