Colleen - I think they leave open set amounts of Palo, shore excursion, and Flounder's times for each booking group. I don't really know that for sure, but I would think that otherwise it would be too hard for 1st time cruisers to ever get what they want.
My kids will be 3.5yo and 11 months on the cruise so we'll see ya in Flounder's! Both of mine will be in Flounder's cause my daughter tried the club on a 7 night we took in February and she did not like it. She loved Flounder's though and they told us that we can bring her back even though she'll be 3 (she was days away from her 3rd birthday on that cruise). We found that by saying she's not potty trained, though she is, that we can book her into Flounder's online so I'm pleased about that.
You can take her into the Oceaneers Club as long as you stay with her, so if you think she might have some fun in there, know that it's an option.
We just bathed my kids in the bathtub on our last cruise (almost 3yo and 6 months) without a problem. I even fit in there with the 2 of them, though it was a tight fit. We're in a handicapped accessible room in July though, so we'll probably have to shower with them. We don't have a bathtub at home so we just shower with our daughter and use a baby bathtub for our son. We have an inflatable baby tub that fits inside a regular bathtub, so if you don't like using the regular tub, that would be an option. I might bring that for my son in July, but I might just end up showering with him if he'll stay seated and not try to stand up and cruise the shower walls.
My only advice about a stroller would be to get a very lightweight one. A lot of the excursions I looked at say that while strollers are allowed you might have to fold it and carry it part of the time. The thought of doing that with a huge, bulky stroller scares me, especially since it will only be my mom, me, and the kids. We have a Peg Perego Centro Completo, which I love and plan to bring cause we'll be in
Disneyland Paris for 5 days after the cruise, but I might just buy 2 cheap umbrella strollers and bring them along to use on the excursions.