Hi DisMom1981,
Welcome aboard!!! You guys are going to have a blast. Your children are going to be very well taken care of in the kids clubs and nursery so do not be afraid of leaving them once in a while. As far as strollers, I do NOT believe they rent, but there is plenty of walking space that you could bring your own for the ship and excursions. I have honestly seen very few strollers on the ship itself. I would not bring the double wide kind, but if the seats are one in front of the other that would work. I hope my observations helped. Your TA would be able to find out for sure.