No kids myself, and not cc yet... but have come know many crew...
I knew of a husband and wife who both worked Long Haul. They were always rostered on the same flights. Had been flying for ages, so very senior. They had two or three kids of different ages but all in school. They commuted to their base about a two - three hour drive. They lived in the country on a farm. Anyway, his parents lived with them, so essentially did everything whilst they were away.
It would be tough whilst both parents are away, but when they are home, they are around 100% of the time.
For your situation, I presume that your partner is able to manage everything while your away. The kids will soon come to know that you are away for a week, but then you are back for 5 whole days without having to go to work at all. This would also give your partner a well earned rest. It will be hard on christmas and birthdays. But then they will always get really cool presents from New York, Bangkok and Tokyo!
Give it a go! If it doesn't work out, you can always go to short haul.