Hi Leez.. You can take either a Grand Class Princess cruise or Voyager Class RCCL.. Both have thing to do for kids. For me it would depend on itinerary. do you want beach time. Check out ports of call and decide. The Voyager Class vessels have all the gimmicks on it, rock climbing, ice rink, mini golf. The Grand class ships will have movies under the stars (one of which will be G or children's show) If your children like parades, Voyager has one a couple of nights but it is very late.
Now my preference would be Princess. It is more refined than RCCL. Food to me was better on Princess. The pools on Princess are fresh water not salt. The pools on Princess are open 24hr.
On RCCL The newer vessels have expand kids club areas. But there is a cost for Jonney Rockets now. I would pick a newer ship for the WOW factor. The bigger ships have more things to do in the age range you have for children.
Find out which one your parents went on because if it was Princess you and them can get ship borad credit if you are new to Princess. They have to submit your name first then you tell your TA that Mr & Mrs Leez recommended you and you would like the newbie credit. Since you have a family of five it would help out.