You are going to have a great time! The Wonder is a lovely ship.
Our kids love the pools but be aware that kids must be potty trained to be in them (no swim diapers allowed)... however, next to the Mickey Pool is the "splash zone", where non-potty trained kids can be (swim diapers required).
There's also the kids' clubs... if potty trained, the 3 yr old can be dropped off there. If not potty trained (and/or if just you want to bring your 1 yr old in sometimes), go to the kids' clubs during "open house" hours. During that time, parents (or anyone, actually) can use the space, which means you can hang out and play in there w/ your kids (and kids can't be dropped off). During "secured programming" (i.e., not "open house"), only parents can come in (briefly) to drop off/pick up kids. Check the schedule (called the "Navigator"- now available in through a phone app, in addition to the paper copy) for specific programming available in the clubs.
I'm not sure what your kids would think of the evening shows. They're very well done, like Broadway quality, but not as long as a full-length musical or theatrical performance. If you think your kids can't sit through the shows, though, you can arrange childcare. Basically, the 3 yr old can be dropped off at the clubs (if potty trained) but the 1 yr old would go to the nursery. Clubs don't require a reservation but the Nursery does, so be sure to plan ahead. I believe if the 3 yr old isn't potty trained, then he/she can be left at the Nursery too, but you'd want to double check. Also, the clubs are "free" (or, as DH always reminds me- "included") but the Nursery has an addt'l fee.
There are also, of course, the meet and greets! As soon as you get on board, read the Navigator (or ask someone) where to go for tickets. They're "free" ("included") but they give out tickets to control the crowds. You'll want to do this first thing, so you don't miss out. They're likely still doing tickets for the character breakfast and also also Princess meet (possibly even Frozen and Pixar meets, too). In addition to those, there lots of other meets, which you'll see scheduled in the Navigator. One tip: I didn't realize that the characters wear different outfits on the different days! If that matters to you, you'll want to be at the meets more than once.
That's all I can think of for the main things to do w/ little kids, but I'm sure others will chime in w/ more. It's much more relaxed, low-key than going to the Parks and for that reason it's the perfect thing for our family's preferred vacation style!