L.M.
I agree that your husband is emotionally abusive, whether he realizes it or not. Obviously his comments are getting to you and if something isn't done about this then he may end up causing your child to have a complex about her weight which will lead to eating disorders.
My advice is to go to counseling. It isn't healthy for anyone to be in this sort of situation. Even if he is unwilling to go a counselor/therapist can equip you with skills so that you can handle the situation.
As far as your husband not believing that taking care of a toddler is a hard job, plan a day out, write down her routine and stay gone all day long. Go see a movie, shop, or whatever. After walking a day in your shoes he may realize that toddlers are a handfull.
You are blessed that you can stay home and raise her. Other moms aren't as lucky. There is no reason for him to be rude. Has anyone told him that he can be really rude?(maybe he doesn't know)