Husband lies, spends, etc etc but now he's cheated. Do I stay or go?

Hi I really need an outsiders perspective on my situation.

I've been married to my ADHD husband for 9 yrs and we have 3 small children. I've always known he had ADD as a kid but when he finished school he stopped taking medication and thought he could cope. He convinced me (and himself) that he didn't really need it anymore.

He has always been hopeless with money, changed his plans constantly, made decisions without thinking, and lied when he thought he could get away with it. But the good times far outweighed the bad and we were happy. I am the yin to his yang and I paid the bills, kept things in check, took care of the children, constantly reminded him of events, etc. 

Until the last 6 months. Things somehow changed. I don't know exactly what started it but we both got more and more stressed, his lack of consideration for me or the kids led me to withdraw from him. He started going out more than usual, at odd hours. He wouldn't or couldn't take care if the important stuff in life. The easy tasks would get finished but anything unpleasant or hard just never got looked at. My resentment for this grew and grew. I decided that I would just start worrying about me, and my kids, and he could live his own life. But I couldn't stop caring so i just kept getting hurt. Over and over. 

Things finally came to a head and i rang him at 1am to see where he was and I told him not to bother coming home. I thought that if he came home then there was hope and we could talk, if he didn't then I'd made the right decision.

he disappeared for two days. Then he came home on the Wednesday afternoon begging forgiveness, promising change etc etc. So I agreed to try. He promised that our family was all he wanted and he'd do whatever he had to to make things right. We took our kids out to a Christmas party and when we got home he headed to bed early. I stayed up still fretting about everything. When I went into our room to go to bed at about midnight, his phone rang. Weird, I thought so I checked it and found all these texts and calls to another girl. All from that day. The day he's telling me all he wants is us, and then calling and texting her while we're out with our kids. Telling her she's the only one he wants and a lot of other hurtful things I don't want to think about.

i confronted him and he tried to lie. I took my kids and left.

its now a week later and he's been to see his doctor who said he needs ADHD medication again, and this might explain a lot of his behaviour. He's full of guilt and remorse and good intentions, but yesterday he asked if it was ok to call me in the evening. I agreed which took a lot for me to do because talking to him is still really painful, and guess what? No call.

Am I fighting a losing battle here? If I go back am I just letting him get away with it? I don't want my kids to pay the price for any of this either. I'm so lost. Any help, guidance, anything would be appreciated.