We took our 15 mo old twins & 3 yo, all boys, on the Rhapsody in Sept, 2004.
We have a similar tandem stroller, it is a little big but, worked great for us.
I don't think a side-by-side would fit through the doorways, etc.
If you have to tender, there are always men there to help with getting the stroller on/off.
We didn't have any problem getting around with it on the ship or in the ports, it was great to have all the extra storage space underneath. In the dining room they always found a spot to keep it while we ate. It was especially helpful in our 1 1/2 days of very rough seas from hurricane ivan!! Have a great time. We also found it helpful to take the
disposable sippy cups that can be washed or thrown away.