Depends a lot on the kids. "Under 12" covers a lot of ground. Are they light or heavy sleepers? Attitude means a lot, too; I don't know your kids, but I've seen other folks whose youngsters ranged from the discipline of young soldiers to diagnosed Oppositional Defiant Disorder. Only you can assess.
If the kids are of an age and demeanor to handle it, intercoms in their rooms and a drilled plan to race to the master bedroom when you awaken them with the order to do so, could work.
A simpler approach would be to plan to make your stand near the head of the stairs. That would put you at an interdiction point between the kids' rooms and the access path of the intruder(s). A large, thickly stacked bookshelf strategically placed there would give you good cover.
You'd be in position to hold that ground until your significant other can round up the kids and shepherd them to the master bedroom/safe room.
Wishing you the best, and appreciating the thought you're putting into this for your family,