I agree with f-mattox that a family of three would be more comfortable in a mini-suite. I speak from experience... our son is a young teen. We were in a BA cabin on Diamond Princess (different ship, cabins pretty much the same) and it was tight as there was no sitting area. That huge balcony was wonderful, and became my refuge!
For our subsequent Princess booking, we selected a mini-suite. The cabin is much larger, still has the huge balcony, and would have given me much-needed privacy within the cabin.
I wouldn't be concerned about the uncovered balconies -- that's JMO, though. When we had our BA on Caribe Deck, we could see the mini-suite balconies below ONLY if we went to the rail and looked down. Everyone was respectful, for the most part.