I really do understand what you are feeling.
If you truly want to make a change, to make things better for you and your children (if you have them), you have to be able to make the choice because it is right and never because you want to be with someone else.
Being alone can be hard but I, and many other women, walked in your shoes.
I got to the point where my husband was like a roommate that I detested. Just the thought of him touching me, made me sick. I literally felt physically ill at the idea of intimacy with him and eventually I just refused to do it at all, even without making excuses as to why. But I waited so long to leave that I had alot of baggage afterward about myself, and lots of self confidence issues, and so on.
You will teach your children a worse lesson though by staying in a situation like that. Especially with a man who is mistreats them, because they will learn to accept and expect that. Then in their own life they may very well make the wrong choices and stay in relationships with partners who treat them poorly. You are the one who can teach them about being strong, about loving themselves, and not settling for less then the respect and love they deserve from someone else.
Don't let what you may feel for some other person make your decisions for you. It is great to feel a connection with someone. But you have to do things for yourself with no expectation of a relationship to follow. Because even if it did, like any other relationship, it might not work out and you'd be on your own then anyway. So just plan to be on your own, till you get your 'feet on the ground'. There will always be time and opportunity for other relationships once you have taken control of your life.
I wish you the best. BE STRONG! I know you can be. I've done it, and you can too!
God Bless you.