I'm pretty sure this is allowed by the airlines, but I won't claim to be sure of every airline's policy. I believe you can be in an exit row if you have young children with you, but seperate cabins is fine.
Assuming your kids are well-behaved, I think this is entirely reasonable for you to do. I would do the same thing if I were you. You should avoid making unnecessary trips back to Y, and they should not come up to F (although it might be allowed).