Make sure that you take the kids to the first meeting of Camp Carnival. There they will meet other kids. Camp Carnival is divided by ages so they will meet the counselors for each age group and get a list of the activities.
Our daughter has been traveling with us since she was 9,she is 15 now, and she always goes the first night to the Camp Carnival meeting, she might not participate in all the activities but it gets her the opportunity to meet others her age. She is very outgoing so she usually has not trouble hooking up with others her age. Usually we have to drag her to dinner with us in the evenings because she has so many other things planned. We let her plan her sea days, she goes with us when we are at port. You kids should have no problems.
By the way, since you are going in June, school is usually out and you will find an abundance of kids on the ship.