Yes, we are in Club World. Unfortunately, we are only Bronze. I will call tomorrow and hope that they agree not to move us.
And you are correct--with the available seats, there is no way for us to both be next to (or in front of/back of) the child on our particular booking. One of us can be next to one child while in front of (or behind) the other...but then the other parent has to sit in front of or behind the other parent.
I really honestly don't know why they moved our seats that one time. It was just a theory. Maybe there was a broken seat.
We were on a flight once where they turned the plane around for a passenger once we had already pulled away from the gate, but it was because the plane had the bag and not the passenger. Everyone was surprised and joked about it being a "VIP" but they literally announced it was because we had their luggage on board due to safety issues with having unattended luggage.