Sure you can go and drop off your baby at the nursery during dinner, I have left the table several times during our cruise to.... go to the bathroom, go get a sweater from our stateroom... once even to go to guest services real quick. The dinners take so long that it was no problem.
Also regarding cancelling the nursery.. technically yes they can charge you if you cancel under 4 hours. In my experience though (well my friends' who had a baby with them) they never got charged if they called the nursery before the start time of what they booked. Anyway this is not a guarantee of course, I would try to give them more notice to be safe.
We also have the late seating and use the dine in play, the youth staff are waiting at the entrance to the restaurant by around 9 and leave at 9:15.
Couple of times we missed them and DH would just run the kids upstairs to the club and be back within 5 min.