We had this issue as well on the Regal. We were next door to a family of six passengers. Supposed to be Mom and child in the mini suite next to ours and Dad and other three kids in the inside cabin across the hall. Well, you know it really turned out to be Mom and Dad in the mini suite and all four kids across the hall. The kids kept running back and forth slamming the doors at all hours. One day the Mom jokingly "apologized" for her kids' behavior, but never did anything about it.
I never thought of saying something to the room steward. I'm sure they'd know it was us who complained.