Is it possible to get a private water taxi from Belize City to Ambergris Caye? Is it a shorter ride? I've been reading about how the ferry can be crowded and long. We are traveling with 3 kids under the age of 4. What is easier...flying or ferry?

Flying is much easier

Also much more costly. If you travel in the middle of the day the standard ferries probably won't be too full. If you travel at the start or end expect them to be packed. But even so it won't be too bad with young kids - what do you think the locals do?

With three kids and luggage I would definitely recommend the flight if your budget allows - under 2s travel free with Tropic (probably the same on Maya) and they give cardmembers 10% discount. If you want to check out the private charter pricing you could contact Coastal Express who may be able to help (info@coastalxpress.com)

Fly

People comparing the prices always seem to forget the expensive land taxi ride from the international airport in Ladyville to the water Taxi terminal in Belize city. Plus its longer, much more trouble and your usually tired after a long day of travel.
catch the Tropic or Maya flight to the island, very little difference price wise and a heck of a lot easier and faster.
Fly

Even with all the Water taxi Timetables on my Belize Water Taxi Guide,

I agree with Elbert, from the International Airport, a Flight to San Pedro is the safest and fastest way to come one the Island.

No hustle with Buses or Taxis, especially with so many kids.
At least you come here for a Holiday, not to stress you self
with your entire luggage and the Kids in the City.