I've done 9
DCL cruises as a single parent...starting on the maiden voyage with a 7 year old...soon to be our 10th trip for her 13th birthday.
The shows, etc. are divided into "adult" and "family." That just tells you whether or not the jokes, etc. are "clean" enough for the young ones. I've never felt out of place, etc. I snorkel at Castaway every time.
Depending on age, DD has been thru various phases of enjoying the club/lab and wanting to hang with mom. We kinda go with the flow. I'm happy to be with her as much as she wants, but I really enjoy my space too. It's a very easy vacation as she can eat when/where she wants, etc. and I don't have to do any advanced planning in that regard. The only thing I've not done is dinner at Palo, which as a single is a little weird. We sometimes have groups like the dis board gang that will do brunch or tea at Palo.
My experience is that her enjoyment of the lab, the stack, whatever is dependent on finding a "buddy" about her age. For our upcoming cruise, she "met" a friend thru these boards. The kids have been chatting on line, and plan to hang together on the ship. If she doesn't make a friend in the first day or 2, she will hang with mom a lot more.
THere is a "singles" lunch and a few other single activities...but I mainly did the family things. The adult programming is great too, and you won't feel at all out of place as a solo.....
Kathryn