Why would turning on one breaker trip another?
Somewhere the circuits have been bridged together where they shouldn't be. And if the hots are out of phase with each other, then turning them both on creates a direct path from one hot to the other, and a short, which is tripping your breaker.

If you're seeing this kind of wiring issue, then there are almost certainly others that are also there, and the proper solution is to gut your house, find all the hidden junctions, fire hazards, and other wiring issues, and likely rewire the whole mess.

Since you'll likely ignore that advice, find the mid-point between these two circuits, break it into two by unhooking the load connection from the outlets on each end of the two circuits, label the line, and bind the hot and neutral together on each end of that disconnected line so that no one reconnects the circuit accidentally. To find the midpoint, start unhooking one side of an outlet and see what still works when you turn on one of the two circuits. And make sure the kids aren't trying to put things in the outlets while you're testing.