Opinions no judgements

I am a 23 year old mom whose been through hell with my sons dad. 
1.he cheated once (that I know of)
2.he has two other children with another female (to which 1 he says isn't his, since at the time he was in jail; which he also says) 
3.he was a meth user
4.he use to hit me, when he was using
He's now trying to redeem himself with me, he says I'm the love of his life & the other girl was a mistake (not his child, just the girl) but at the same time idk what I should do here I'm at the point where I care & don't care at the same time. He hits me up every day checking up on me & my son & cheering for me cause I'm back at school & raising my son when he hasn't been there 
Does it sound childish that I'm even giving him the opportunity to change once more ? 
-He has a place to live in
-he says he's willing to do whatever I ask of him 
-& he's already in the process of getting a job 
Oh & im not planning on in moving in with him or nothing till I see change (it'll take time obviously)