OP,
I am an RN. For the 1st 2 years of my oldest girls' lives I was a single mom. Their biological father chose not to involved with their lives. I could force him to be financially responsible, and I did, but I couldn't force him to be a father. For 3 years it was all me. I got up at 4am, got myself ready, got 2 babies washed, dressed, and fed, dropped them off at daycare at 6:15 AM, worked a 12 hour shift, and picked them up at the babysitter's at 7:30 PM. I did this at least 3 days a week for 3 years. In addition I did all the other things that needed to raise children and keep a home. It was exhausting.
When I met my now husband and we discussed marriage I was very frank with him about what I wanted, needed, and expected from a husband and a father. I didn't want just a check, I had that. I didn't want someone who was just going to be the fun daddy. I needed a partner in all things involving raising the children I already have, and any more we might have. ...and there have been 4 more.
We split things, because I made it clear to him that that is what I needed to out of a marriage. We don't have any hard and fast rules about who does what, but it kind of works out for us. I do more cooking because I'm better at it, and enjoy it. He does more cleaning because he is fussier about it. He does more yard work because he enjoys it more, I do more laundry. We split child care and raising evenly, based on who was available and for whom it was more convenient. He makes a lot more money than I do, if that matters. I went back to school and got a master's. He supported me emotionally, and although it was hard with a big family and a job, and although he did pick up a some slack, because there were days I had classes, I never used it as an excuse not to contribute. I worked my schoolwork around my obligations to my family.
This kind of informal arrangement works for us because we agreed long ago to be partners. You are in a position where your husband is not pulling his weight. You need to sit down and have a frank and concrete discussion with him about what you need in regards to making your family work. For you it may even be beneficial to make a chore chart and assign chores (my kids are bigger now, we can farm a lot of chores out to them)
Being constantly exhausted and resentful is going to take it's toll on you in terms of being a good mother. If you aren't happy it will come through in you interaction with your daughter, whether you intend it to or not. I remember those early years being tired and stressed and angry with their father for not being there. There are times when I wished I would have been able to do more things with them other than trying to entertain them while trying to get housework done. Times where I wished I was more patient with them instead of being exhausted and easily annoyed.
You are fortunate, you have a partner, you need to find a way to make him be a partner.
