How old are the kids?
Mine are 5 and 2. They do NOT sit still well, and they would do no one any favors at all in a church or at a viewing. Perhaps your family is different than mine, but when my cousins' father died, they were grateful that I didn't attempt to make the kids sit through the funeral. They would have preferred not to have their OWN kids there. In our family, the life is celebrated at a family gathering after the service, and the funeral is a sort of necessary ceremony. Until they are old enough to understand the solemnity of the situation, this is no place for kids - they can come to the reception later.
However, your family sounds like a different culture, or at least has different customs. Perhaps, his family is more like mine, and it was HIS family custom to not have children there? In which case, maybe he truly doesn't undertand. So, explain it to him. Children are ENCOURAGED to go.
But, he "doesn't want the kids around any of (your) family"? That is a bigger issue. Holidays? Birthdays? Anything? What is going on? If this is really a bigger issue than this particular funeral service, then you guys are long overdue for a discussion, anyway.
I am sorry to hear of your and your family's loss.