Heard this joke?
One afternoon a man came home from work to find total mayhem in his house. His three children were outside, still in their pajamas, playing in the mud with empty food boxes and wrappers strewn all around the front yard.
The door of his wife's car was open, as was the front door to the house. Proceeding into the entry, he found an even bigger mess. A lamp had been knocked over, and the throw rug was wadded against one wall. In the front room, the TV was loudly blaring a cartoon channel, and the family room was strewn with toys and various items of clothing. In the kitchen, dishes filled the sink, breakfast food was spilled on the counter, dog food was spilled on the floor, a broken glass lay under the table, and a small pile of sand was spread by the back door.
He ran up the stairs, stepping over toys and more piles of clothes, looking for his wife. He was worried she might be ill, or that something serious had happened. He found her lounging in the bedroom, still curled up in the bed, still in her pajamas, reading a novel.
She looked up at him, smiled, and asked how his day went.
He looked at her bewildered and asked, "What happened here today?"
She again smiled and answered, "You know every day when you come home from work and ask me what in the world I did today?"
"Yes," was his incredulous reply, half shouting.
The smile remained, "Well, today I didn't do it."
He sounds a bit dim - perhaps he needs to be shown the obvious? Which, btw, he shouldn't need to be, because he should TRUST you when you tell him how hard it is having a small baby and running a house.
Could you put aside a Saturday or Sunday, tell him what you normally do on a weekday, and then have him do it all, plus have dd, only bringing her to you for feeds - he has to wind, change etc. Oh, and ditto the night before so he does it all on a night of little sleep.
And remind him that, as someone who carried a baby for 9 months and is breastfeeding, there is no way he is as tired as you at the moment.
I would spring a surprise repeat performance on on the Sunday too, if he's in the slightest way cocky about it.
He doesn't sound very interested in his dd, and very lazy too. And I don't know why you feel you're being disloyal when he isn't living up to his responsibilities as a husband and father, not supporting you, and that's a kind of disloyalty too, isn't it? Poor you. 