Definitely see a lawyer and get your ducks in a row.
When my ex and I first started mediating, he wanted every weekend too since he works during the week and couldn't do 50/50.
I know your kids are young, but that's not great for you later on. The kids will go to school all day during the week, and then when they finally come home, it's homework, bath time, dinner, dishes, off to bed, do it all again the next day.
Then he gets the weekends which can be care-free, responsibility-free, and totally focused on having fun with the kids.. And that's completely unfair to you.. You deserve fun time too..
I think all the custody rules are different when there is a nursing baby. There's no arguing who the baby needs to be with..
And he shouldn't have ANY overnights if he can't provide acceptable sleeping arrangements for them.
Just some things to think about for the future and how to word your parenting agreement.. You may want a different career later that follows the children's schedule more so that you can be home for them.. How you want the schedule now is probably not how you are going to want it when they go to school. You need some quality time with your kids..
And I'm proud of you for taking steps to keep yourself healthy. Keep it up