I haven't seen many reviews by families with small children, so thought I might have something to add. I cruised with husband, my two daughters (ages 1 and 3), and my in laws. I had done quite a bit of research ahead of time, and Royal Caribbean was billed as a fairly family friendly cruise line, so we went with it.
Embarkation was a breeze. We had done online check in, and when the RCCI employees saw us with the two strollers, they shooed us right to the front of the line, and we got right on board. The buffet was already open, and we were greeted immediately by a member of Adventure Ocean. the RCCI kids' program. They immediately outfitted my three year old with a bracelet identifying her in case of an emergency, which I thought was great.
We had booked 2 adjoining cabins, because it was less expensive than booking a suite. The other members of our party were next to us too. It worked out great. The accommodations were standard - clean and functional, no WOW factor at all. The adjoining rooms gave us lots of space to spread out and unpack our things. We had the girls in one room with portable bedrails on the bed, and we were in the other room. It was nice having the extra bathroom just in case of a "potty emergency."