D.B.
Yikes. This is not a financial arrangement, it's a relationship. Or it's supposed to be.
He's away on weekends, and you thought he was working, but he's gambling? And you're worried about dividing money that he says is his to spend as he wishes? I can't believe you are on maternity leave but there are arguments about how much he pays for holidays vs. what you put in!
Usually, I suggest that men who don't value what at-home moms do all day long simply be given a fun opportunity to experience the easy life. So normally, I would say that you should go away for the weekend and leave him in charge of kids and meals and laundry. Usually that straightens up men who think it's all a piece of cake. But in your case, you have an older child who isn't his, and a man with a gambling addiction. He might be far too neglectful for you to trust him as a parent.
Counseling, now. Financial advisor, now. Get into some support for spouses of gamblers. You're just not dealing with the gambling here, and are more focused on who is paying how much. The gambling and the lying are the elephants in the room, and they must be dealt with. That doesn't mean you telling him that he's wrong. That means you controlling only what you can - which is YOU, what you'll put up with, and what your next move is. But first things first - your baby's financial future needs to be protected. You need to start separating your finances so that your partner doesn't gamble away everything you need for those children.