We were just there Sunday with our 14 month old and our almost 3 year old. You have picked a great time of year to visit as there were no lines for anything and the place wasn't even close to packed. It was a really great day.
As far as the stroller thing goes, there is definately enough room for a double jogging stroller. We brought our double stroller, but our oldest ended up walking most of the time. There's just too much to see and do for an older child to keep getting into and out of the stroller. The front seat ended up being used for storage, which was also nice.
My kids were too small for any of the rides, but they LOVED all the animal exhibitions (even my 14 month old). You can feed the dolphins and/or the sea lions for $4 per tray of food. We also saw the Shamu Believe show which was really awesome, and my oldest couldn't take her eyes off of the water. When it was over she was walking away with head turned back toward the water waiting for Shamu to fly out of the water again. My youngest had a bit of a hard time sitting through the show though. Thank goodness it was only just over 30 minutes.
Anyway, hope this helps you out. Have a great time!