OMG i'm sorry that you are going through this, i've watched it happen for 10+ years.
You could be my sister! He'd do the same thing, every month. But he'd go on these benders and drink up their bank account leaving her with nothing to buy food, gas, etc. Thank god for my Dad, he was always there to help her. He'd cheat all the time, always coming hom a week after he left, broke hungover and sorry.
But she'd take him back.. over and over.. Oh how i hate that stupid worthless man!
I think that maybe it could be, that you want the challenge of changing his behavior? If you do want him to change, you will only get hurt trying.
I seriously don't know what to tell you here, i've witnessed what your going through . He sounds like my sisterss ex-husbands twin. The only thing i can say honey, is if you haven't already left him for good, RUN! What he's doing to you and your kids is VERY damaging, you deserve some one who is going to treat you and your kids right, and eventually be a father figure to your children.
I don't know, i could never understand why my sis would take him back. I think it was because she had so many kids with him, and was somewhat dependant on him, but maybe not, because he was always losing his low paying jobs. She claimed she loved him, but the more he did it, the less she cared. And now that she's gaining some independance she's found herself someone new! It still stumps me to this day...