You are a very patient person. I would have totally lost my mind with him by now but that is my way at times when I get really frustrated.
I know how you are feeling. With my first marriage many years ago (16) I did everything for our daughter and I worked full time as well. I was young and allowed it to happen and by the time she was about 18 months she wouldn't let daddy do anything for her, including diapers/baths, help with toys, etc. All I heard was "Mommy Do!!!" We did end up divorcing when she was almost 5 and she had to deal with Daddy during visits and was forced to allow him to care for her.
With my second marriage 2 years ago and the birth of our son 9 months ago, my new husband tried the whole "the poop is gross, I'm going to throw up" drama and I just made him do it. I was so afraid that my son would end up like my daughter, only wanting me since I'm now a SAHM too that I really have made him pitch in. My son can be comforted by either of us now and that is such a relief to me but it took some time to get here.
I would totally use your pregnancy hormones and the pending birth of your daughter to tell your husband flat out how you feel, in the nicest way possible that you expect his help, no fights, no arguing, he will help, it can't be a wait and see thing. As if there is a question as to whether or not you will "need" his help. It's only fair, these children are half his and when he is around he should pitch in too!
I wish you lots of luck!!