Am I moving on too soon?

Your ex is jealous. He expected you to sulk and hurt (forever) over the break up just to feed his ego--everyone wants to believe they are the onliest. You aren't playing his game the way he wants you to so he's attacking your character because he's immature and doesn't realize he's not making any brownie points that way. You've waited 3 months and now are slowly beginning anew--good for you. If your ex truly wanted you back, he wouldn't be calling you names. If he cared for your girls he'd try to avoid any hostility with their mom. It really is too early to be certain about the new love interest so just take it slow, get to know the new guy well, how he reacts under pressure, whether he's stable and dependable (which is important for kids), how he handles difficulty and confrontation. Your girls are still very young so knowing that the guys you are dating are kind and respectful to them is important but you are right to not involve them very much until you narrow the field down to the real possible ones. It is good for your kids to know their mom is carrying on and being strong, moving on to something better because it shows your girls that women don't have to put up with a bad relationship, can take back control of their lives and find something/someone better. The new guy, even if you'd just met him (which you didn't) would still be a good thing. You do have to relearn how to date and reconvince your heart that there are other guys out there who might be a better match. Your ex probably never expected you to attract someone new so fast--but too bad for him. He should have treated you better, should have been more dedicated to you and your kids. He blew it.