Maybe phrase it as, either I can cover the childcare while you’re at work and you cover the house finances, or I need to get a job and we’ll need to pay for child care together. Might help him see that you ARE working, and that making sure your kids are cared for is both of your responsibility
I think you both need to sit down and have a conversation. It is pretty bad that he doesn’t help especially with now with two kids. If he is your fiancé and doesn’t help out with kids that most definitely is a red flag and you should consider it before you marry him.