We decided to go on a cruise with our two children (ages 1 & 2) and our best friends and their two children (ages 1 & 5). We got rooms next to one another in a Family Room with veranda room and enjoyed our time on the boat. Here is what I learned about both the ship and traveling with young children.
1) Our veranda partition could not be moved due to the fact that we were on the end of the boat. Other partitions can be moved, however.
2) The service on Celebrity Summit was amazing. We were in concierge class, but everywhere on the boat the service was top notch.
Our cabin was a decent size for a cruise cabin, but was very out of date. Our veranda had many signs of aging. It was at the end (Aft), so we had great views, however our wall around was not see-through, like the others, so the children had a hard time seeing out. I didn't let my kids out there unattended, as there are lower rails on the far side that my kids could possibly climb on. The veranda partition could not be removed, which was a problem for us, but probably wouldn't be for others. With an update, I would recommend the location and size.