I'm a single mom because I left an abusive relationship. Actually, if you go to the single parents forum here, there are several women in this situation. Is it hard? Yes. It is scary to leave. But it also gets better. I am one year out of my relationship and DD and I have a new normal, I am getting counseling and building a new life. I am sometimes lonely for a relationship, but hardly at all. I think about it and dream about it some, but I really have no desire to actually put myself out there and take a chance again.

Some day I will. But being lonely is the least of my concerns right now. And TBH, I am having too much fun enjoying DD's toddlerhood to want to give up this precious time together and put all sorts of energy into starting a new relationship. StormBride is right, it's actually less lonely outside of abusive relationships in many cases.
FWIW I didn't tell my parents that DD's father was abusive. I said I left because it wasn't "good". Leave's a lot up to interpretation. I didn't tell them because I was not sure how they would respond, I didn't want them to freak out or to feel sorry for me, etc. It wasn't to protect his standing though, more about my own pride.
I agree with the PP's, you should leave. Please google "cycle of abuse", and here is a
great article that might also help. There are also many resources out there to help you and your DC get to safety.