TD visa for children

From an immigration standpoint you need nothing, it's a standard application. However under Canadian law you would need the consent of the other parent if you have a joint custody order, check with a family lawyer.

Immigration will definitely ask to see a letter of consent from the non-custodial parent that approves to move the child to the US. Even just for a vacation, they'll ask if the non-custodial parent is aware that the child is leaving the country.

Lots of parents kidnap their kids and try to cross the border, so I do believe it is law now for them to make sure the other parent is aware of the travel.

Yes I was watching Homeland Security USA and they did exactly that for a woman crossing the border from Mexico. My mistake. But I'm pretty sure you need consent (or at least notification) to move anywhere, even in Canada, not just the US. The other parent has to be informed of what the residence address is.

Yeap, and if no consent, kids don't go.