I'm sorry to tell you, but if you haven't booked yet and want traditional seating you may out of luck
! Traditional books up very early!
As Jim130 said, if you have Traditional seating your kids really should not eat in the Anytime Dining room. This would cause a wait for the people who have booked Anytime Dining and leave empty seats in Traditional, which many people want.
According to the "rules" if you book Traditional and go to Anytime, you lose your Traditional seating (this doesn't seem to be well enforced, so they may
be okay). When you go to dinner the Matre' Di will check your cruise card to see where you're supposed to dine and may
refuse them entry to the Anytime Dining.
If the kids don't want to eat in the dining room there's always the buffet or the pizza/hamburger restaurant.
Have a great cruise, wherever you eat!