Many people do 4 in a room as you are questioning. It is a cheaper alternative for sure but the drawbacks are obvious. It will be crowded in the room and you'll have 4 people competing for the bathroom. On the other hand you'll have more space with two rooms and two bathrooms but then you'll either have to split up the kids and adults at night or worry about your kids sneaking out of the room after you've gone to bed.
Carnival or Royal Caribbean would be the two lines I would recommend for the kids and I guess Carnival first because of the larger rooms. But the Voyager class of RCI has a bunch of stuff for the kids to do.
I'm going on a Carnival cruise with a camily of for (18/15) and we got one room with an oceanview, space might be an issue, but it was alot less money. Carnival was suggested to us becuase of hte laid back atmosphere (my family doesn't like very elegant things) Carnival ships have lost of things for kids, the newer ships have mroe like a teen dance clue arcade ect. The Voyager class ships on RCL are also good, you might want to put a post on the TEEN MESSAGE BOARDS
We took our daughters (16/7) with us last year on the Carnival Spirit and had adjoining balcony cabins. It was wonderful to have the two bathrooms. We left the door between the cabins open and it worked out great for our family. I had planned to get a suite, but it ended up being less expensive to get the adjoining cabins and the extra bathroom was a huge plus!
We usually travel with just the younger daughter (the older one is my stepdaughter and she usually visits her mother when we travel). When it's just the little one, we get one balcony cabin, but I wouldn't want to have all four of us in one room.