Help!! His ADD is driving me insane

I have been with this guy for nearly 2 years now, i have a 9 year old son (not his) and i have now a new little baby to my partner. whilst i wads pregant things were very hard as i was working and he could not hold a  job down. During this time when i was pregant we nearly lost our house, wass selling our furniture to pay the rent as he was really bad with money. he would continually buy and buy things we didnt need, BUT he had to have these, once he bought them he would find something else he would need to buy. Drove me insane. We were constantly fighting and his drinking habits were not helping. He would drink as soon as he got up in the morning till bedtime. he would leave half drunken bottles around the house and then reopen another beer as he forgot where he put his beer. Our arguments were full on, as because i was working i would come home expecting a clean house and everytime looked like a bomb hit it!! He did not work so my expectations was for him to have the house clean, dinner cooked but neither ever happened. The more frustrated i got at trying to get him to understand that i needed him to help me made our arguments turn towards violence with him. He would grab me and throw me around the house, throw punches (which luckly never hit my face directly), break things at home, scream like a child at me and pull my hair. It got to the point where i wanted out cause i couldnt handle the stress of the relationship. I was pregnant and he decides then to tell me he had ADD. Our relationship was so bad that my doctor made me go to counselling to help me as she thought i was suffering from depression whilst pregant. Thats when he told me he had ADD. I had no idea what it was and i felt robbed that he never told me about his condition and now i was battling with my emotional wellbeing and a baby on the way. 

Since then i have read up on ADD and realise that some things are just part of his behaviour. But i find it hard to make the relationship work when he is constantly arguing with me over petty little things (and believe me he would make a scene), he wouldnt care about people who are around or at our house he would go that next level to make things worse then what they are. Its embarrassing that friends and family have to see this happening in front of them, which just makes them uncomfortble. I have asked him to stop drinking as it wouldnt help with his medication (ritlin) and to start going to the gym to help with his frustrations. He lies to me and tells me he has taken the medication when clearly he hasnt. He reckons the medication makes him feel funny so he doesnt want to take it. So frustrating for me when im fighting with him everyday to make sure he is taking it! When he is on the medication he is not frustrated, calm and can think properly!! Im am just sick of the fighting, lying, spending and its taking its toll on me and my kids. i need help, do i need to just let him be and have his tantrums. I dont want my kids seeing the constant fighting, its not healthy for them. should i just leave?