The kids might or might not want to attend the wedding. That really isn't the point.
One brother might decide to have a child-free wedding.
The other brother sees this as such an insult that he is wiling to risk his relationship with his brother by not attending the wedding.
If there aren't underlying issues, I think the brother getting married, and his fiance, have every right to decide who is on their guest list.
The OP's husband has decided, in advance of getting the invitation, that because his kids are part of the family and don't cause problems at other family functions they deserve to be invited to this wedding.
Of the two, I'd say the brother getting married has the stronger case. The OP's husband is making a lot of assumptions.
1) That all members of the extended family must be invited to the wedding.
2) That children are being excluded from the wedding.
3) That children are being excluded from the wedding due to their behavior.
4) That his children will behave properly at this wedding.
As a kid, I was invited to all the weddings on my mother's side of the family. All two of them. Because Mom's side of the family is about 8 people.
However, I didn't get invited to weddings on Dad's side of the family until I was 16. Mostly because Dad's side of the family is huge. A line had to be drawn somewhere to keep guest lists to a reasonable size. There were even weddings where my older brothers were invited and my younger siblings and I were not. My parents would ask the older brothers if they wanted to attend. They never did, and my parents went by themselves.
Would I, as a 12 or 14 year old girl, have liked to have gone to those weddings? Yes. Was I hurt that I wasn't invited? No. My parents were very good about explaining, very matter-of-factly, that not everyone gets invited to everything, and that someday, my turn would come. Does it bother me now that I was excluded? Not at all.
As a kid, so much of what I was allowed to do depended on how old I was. Taking out library books on my own card, where I could ride my bike, how late I could stay up, whether I could go out to restaurants with my parents, what chores I did at home, what extracurricular activities I could do. Getting invited to weddings was just one of a zillion things that my age factored into. I didn't feel alone or outcast from the family because of it.
The OP's husband has every right to boycott his brother's wedding. But making that choice, when it will probably be obvious that he could have easily attended the wedding if he choose, will affect not only his relationship with his brother and the brother's new wife, but most likely his relationship with their parents, and very likely with some other relatives as well. This is one of those cases where you *can* do something, but you might want to think long and hard about the results before you do.