Hello Augusta- We are going Feb, its our 2nd time at that time of year because its quite quiet, and weather is more bearable! Also its cheap!
Went last year with Kenwood, going this year with Disney direct. Virgin always seem to work out more expensive.
Are you planning on staying onsite? I would recommend it if you can afford it, makes it very easy with kids.
A common deal is 2 weeks 'unlimited' tickets (so you can visit any Disney park/waterpark at any time) for price of one week, including the dining plan (i.e. free food), if you stay in a Disney moderate or deluxe resort. This will include transfer on the magic express, and free shuttle buses between parks/resorts during the holiday.
For comparison we paid just over 4k for 2 weeks in late Feb flying Virgin, staying at Old Key West villas, with unlimited 2 week tickets & dining. Which I think is not bad!
Caribbean beach is a good moderate resort with young kids because they have nice beaches and a good pool. I know lots of people love Port Orleans -but we haven't stayed there yet!
Most resorts show an outdoor movie around 7pm - you can sit and eat/ have a few drinks while the kids watch, if you have had a long day at the parks. All resorts are VERY family friendly.
You will definitely need a double, or two buggies! This will be essential- they are free to bring on Virgin flights.
2 and 4 is maybe a little young but I bet they will love it- just buy the Unofficial Guide to Disney it explains everything!