Sea Princess do cater for 4 year olds. She/he will have her/his own little club to join - Princess Pelicans. I'm also pretty sure that if you feel that you want adult time on terra firma, you can leave your child with the kids club and they will entertain and even ensure she/he is fed!
Your 4-year-old can join you in the main dining room. There was a large family on the table next to us on Sea Princess at Easter and our waiter was excellent with them all. I'm certain that they provide a children's menu in the main dining room too; that's what Emmanuel, our waiter told us! Children can go into the shows and the bars, obviously as long as they are with an adult. But be warned, if there are comedians on board some of the jokes can be towards adult themes.
Sea Princess used to be an adults only ship for a couple of years for P & O until 2005 so they had to have a little refit to include children's facilities. Therefore these aren't as extensive as other Princess ships. Children's facilities are on Riviera Deck on Starboard side. The splash pool is at the Bow of the ship on Sun Deck, which is a lovely, quiet little area for adults to sunbathe, whilst keeping an eye on their little monsters in the splash pool!
Thank you for the advice, I do feel a little more reassured now. We cruised many times with P&O up until 2003,which happened to be on board Adonia but as you say that was child free then. As it is our first return to sea with our son I want things to go as well as possible. We will certainly be seeking out the facilities on Riviera deck. Is that where 'Easy like Sunday' used to be?