Hi Jamie,
What a wonderful gift ! When my son was 8 months old, he took his first cruise - and at that time I had a two and a three year old as well. Oddly enough, the cruise was one of the easiest vacations we've ever taken (comparing to our WDW vacations).
What is really great about cruising with little ones (especially when traveling with extended family), is the ability to participate in as much or as little activity that you and the kids can tolerate. It is wonderful knowing that the calm solitude of your stateroom is just minutes away at any time. Also, unlike most any other outing with a baby, you don't have to carry a diaper bag, because you can be back to the room quickly for those changes. There are no bus schedules to figure out, or dining reservations to make - it's all there at your fingertips.
I'll also mention that for our family, vacationing with infants and toddlers on the cruise wasn't about "doing it all". Rasing kids is hard enough, especially with an infant - so we viewed the cruise as the opportunity to take a break from the dishes, laundry, cleaning, cooking - and simply get rest when we could and enjoy the family time. We didn't feel compelled to participate in all of the activities, we didn't even get of the ship while in Nassau - we took advantage of a relatively empty and quiet ship. So take this vacation, and remember that regardless of who paid for it - it's your vacation.
Awhile back I answered a question with a few of my "must haves" when traveling with little one, you can see it
here. It is also worth mentioning that if your almost-3 year old is not potty trained, they will not be permitted in the swimming pools. There are splash-grounds on each ship that are suitable for children in swim-diapers.