We have used Camp Carnival on 15 different ships (including the Pride) without a problem.
You will not be turned away.
On the embarkation night, there will be an orientation so that you can fill out one sheet of paper listing allergies etc. It is usually around 7pm, so look for the notification in the Capers.
Later on in the evening there will be a gathering (including parents) so the kids get comfortable with their counselors.
Camp Carnival starts the next morning at 9AM. And they care for your little ones until 10PM with breaks for lunch and dinner. Port days are handled a little differently as are formal nights (in case parents want to eat alone).
It will all be spelled out in the CC Caper that will cover all camp activities for the entire cruise. (unlike Adult Capers which handle one day at a time)
Camp Carnival has always exceeded our expectations. We have a special needs son and (I admit it) I am WAY overprotective. They have always done an outstandng job.