I don't know if you can do it for under $2000. Here's our situation:
DH and I are taking a cruise in January. We got, pretty much, the cheapest 4 night available at $399/person (though I think your second child is cheaper...and you can sail for 3 nights at $349 a person for off-season). We aren't using Disney transport or insurance, which meant our cruise for Cat. 12 came to $865.
Cheaper Insurance from another source with better coverage ( a must for cruising) will be about $75.
We're renting a car at the airport, using it at the parks, and dropping it off at the Port Canaveral Budget. Then picking it up again the day we disembark and driving it to the airport to drop off. Using the Costco code, it came to $108...which was about the same as using Disney transportation, but we can arrive earlier and it would be cheaper in your case instead of paying for 3 transfers.
We're staying 3 nights at Pop at $88/night.
No cost for tickets b/c we have leftover passes...you'd of course have to buy those.
And the costs that are just for two, meaning yours would be more: cruiseline tipping for 2 people, plane ticket for 2 people (about $300 total) , eating cheap at the parks.
Our MUST costs came to $1900.
This doesn't include the cost of: excursions, drinks on the ship, souvenirs, photos.
So when you add in your third person for cruise, tickets, food, etc. I'm not sure you can do it for under $2000.
BUT, I can tell you that I signed up for the Disney Visa...that gave me $50 free Disney dollars and $50 on board credit on the ship if you put the cost of the cruise on the Visa. It also gives you 6 months to pay the cruise off, interest free.
Good luck to you, I hope you can make it work somehow. Maybe just the cruise or the parks?