I agree that you should not ask him to help.
Do you both see childcare as your responsibility mainly? What about housework?
He provides financially but so do you OP. You have an actual financial worth which can be measured in pounds sterling, the same as his financial contribution does.
If you were not there, how much would he have to pay for the childcare you do, chauffering, cleaning, laundry, personal shopper, cook, gardner, etc.
So, get that basic idea into his head. You both work. You both make financial contribution to the house. You are both busy during working hours. You are both tired at the end of the day.
Then, look at how much free time you both have. Is it roughly even? If not, that's the bit you need to fix. His hours will be something like 8am - 6pm Monday to Friday? Yours are something like 6am - 7pm with additional nightshift 7 days a week? When he is away he is working longer hours but you are working 24/7.
You will both have 'downtime' during the day when you can have a break, coffee, lunch, etc. However, he gets to do all that without young children wanting something. He can commute in peace, he can sit down to eat without interruption, he can go to the toilet without having to carry on a conversation at the same time!
When you break it all down and look at it reasonably, you can see that he is not pulling his weight and this needs to change pronto. The more you carry on like this, the more he will expect it.
Btw who has said you are 'whining'
? A whine is when you draaaaaag yourrrrrr woooooorrrrrrdddddssssssss oooouuuut in a high pitched voice. You are not doing that. You are stating that his behaviour is selfish and he doesn't like to hear it so he tells you to stop whining. Am I right? That has to stop, he is being disrespectul and immature.