It sounds like you really need to talk to your priest. He will be able to help you access diocesan resources, as well as knowing a lot about community help. Same thing with the parish staff – a lot of times, the Parish Secretary knows everybody and everything!
The most important issue would seem to be getting a new custody ruling, because a sex offender who hurts kids is not supposed to be around any kids. Solve that first.
Next, you obviously need friends. Get to know other moms. You will not feel so lonely.
After all that, if you have time and energy, maybe start worrying about an annulment. (Okay, you probably want to start the process as soon as you can, just to get it off your plate, but you don’t need to hold your breath.) And then start worrying about dating, when you know what is what.
Honestly, you have a lot on your plate, and you were already with an abusive nogoodnik once. So having time to clear your head and see how normal couples work would probably be a good idea.
I mean, you don’t want to panic and pick the first guy who comes along, right? Especially since you have kids, you will have to be picky and take your time. So since things are so busy anyway, take that time as a gift.
(And if you get an annulment and are able to move home, you would not want to be stringing along some poor guy, right? Better to wait until things are settled.)
That said, and obviously I am not a canon lawyer, I seriously doubt that you would be unable to get a marriage annulment. A guy who molests kids/girls probably did not enter marriage in good faith, or believing that there was nothing wrong with him. Also he is likely to have pulled other hinky things, which all might affect validity of his consent or yours. Talking to a canon lawyer as well as a priest is what you should do about it, because even your priest may not know all the annulment stuff.