Having been on now 3 cruises with my toddlers (2 since the COVID restart), I think I have some experience. First, don’t expect your kid to act anything like they do at home. My normally super chill laid back kid is a nightmare on vacation, whereas my super needy and demanding 2 year old has been a blast on cruises.
the first day you get on the ship, go to the buffet aNd ask for a few cartons of milk, the waiters will bring them to you without an issue, and just leave in the fridge. First breakfast, take a few extra cereal boxes as well to have a snack. My kids drink milk before bed, so we’d always grab extra milks at breakfast.
Take a good lightweight stroller, one that reclines so can be used for naps. I’d personally skip on the inflatable tub because my kids really didn’t fit in them after a year, and my kids are small. Those inflatable tubs are tiny. My kids still hate showers and hand held showers, I just wash them super quick and deal with the screams, and pray no one is going to call security. Also just don’t give them a bath every day.
Pack some new toys to keep them entertained and pull them out at different times. I’d usually give something new at dinner. And I don’t think any other parent will be judging you for using the tablet, that’s basically the only way we can eat at a restaurant on the cruise.
Make sure you request a pack and play in advance, and bring your sheets. I’ve asked my room steward for some extra flat sheet to fold up and put on top of the pack and play mattress because it can be a bit hard, and then just put my own sheet on top. Also if he’s used to white noise, bring it on the cruise. I just use an app on my phone.