I think he has totally used you. He has been a cocklodger in the truest sense. To move in in less than 7 weeks because he needed somewhere to go
and then almost immediately move out again because he's met someone else? WTAF? 
I'm only 21, I feel young and silly
Very young yes, maybe not silly but certainly misguided and naive. You cannot move a man in after a few weeks when you have children my love, you really can't. I know it's tough being lonely and coping on your own but clutching at straws and referring to a guy as your 'DP' after only a few weeks is madness, and damaging for all of you. 
Please don't do this to yourself and your children. Certain types of men can sniff out a needy, vulnerable woman a mile off, and will take advantage relentlessly if you let them. At leaf he's being honest with you, which is better than the alternative of sticking around out of convenience while shagging someone else.
You've rid yourself of one abusive man and survived to tell the tale, so you can TOTALLY do this. hold your head up, let him go without a fuss, stay strong now and get keep your little family strong, just the three of you for a while. Don't beg this man or wish for him to change his mind - if he does it will only be temporary. You really don't need him, you have everything you need right there already, in your children and in yourself.