I wish you luck on your trip, but there a couple of things you need to think about, such as distance from an airport, roads closed due to snow.
While I love the Big Bend area, it will be tough during spring break. TX spring break is either the week you have or the week before and it is full of people. I was going to suggest the Padre Island area, but that is going to be worse than Big Bend.
If you don't have a reservation for a campsite in the area, you probably won't find a site within 2 hours of the park.
The North Rim of the Grand Canyon will not be open until the end of May or into June, depending on snow pack.
I think you need to determine which airport the kids are going to use, Big Bend is 4 hours from Midland, which is the closest airport, not sure which airport serves the Grand Canyon, but it is probably going to be at least 4 hours one way.
Good luck with your trip, safe travels
