OP, this man is not respecting you as a mother. I've been a fifo partner and a mother with a new born for a short time (with DP being away for 4 weeks at a tim) and yes they are working hard away, but you are also the sole carer for the children when they are away. 24/7 no nights off, plus you have to handle everything on the home front all alone. No one to help you carry the groceries in, no one to help when the kids are sick and so are you.
Working, as well as having young children while being a FIFO widow is bloody tough. If my partner had continued fifo, or goes back to it, i won't return to part time work while my DS is small.
That email was just disgusting, i would not be sticking around to put up with that.
You ARE working, you are raising the children. If he earn's plenty of money to keep the family afloat, there is no need for you to work while your youngest is small.