When my eldest was a baby, I had to go back to work and he was with a childminder, but outside of that we both cared for him and the housework, when we found out no 2 was on the way - my husband gave up work and looked after my eldest from 10 months old and then the 2nd when he was born after I went back to work. Leaving him with two babies! When I was home we shared the work and when he worked part time, I had the kids while he worked and vice-versa. He went back full time when they both went to school. We have always shared everything as far as possible - During the week I finish in time to collect them from school so do more of the childcare, but he will take them out swimming or something at the weekend while I catch up on housework or whatever, neither of us has any problem looking after them - although he has got a bit more out of the habit now that I do all the packed lunches etc, as he now claims he has no idea what they like on their sandwiches! Cant complain though as he does all the ironing and is responsible for keeping the kitchen dining room and utility areas clean and tidy and that includes dishwasher responsibility!
I think times have changed now and fathers are expected and want to do more in their childrens lives.
Is your BIL genuinely lazy, or does he just feel out of his depth with small children and feels uncomfortable about admitting it and learning what to do?