You might want to call and see what ADRs are even available and make your decision from there. Not only is your trip very soon, but throw in
free dining and you may find that there aren't a lot of choices available to you.
But I also agree with the PP, if your plane is getting in at 2pm, you shouldn't expect to be at Disney and checked into your hotel for a few hours. You still have to deplane, wait for your luggage, go get a taxi or rental car or wait for ME, then it's about a 30-40 minute drive to the resorts in the best of traffic (and remember with ME you may be stopping at several other resorts to drop off other passengers), and with all that you'd probably be arriving about check in time, which means that there could be a bit of a line ahead of you. Then you'll get your room key and I would imagine you'll want to at least unpack a few things.
EPCOT has a lot of really wonderful Counter Service restaurants that don't require a reservation....so your family can still enjoy an evening in EPCOT but not need to worry about making it to a reservation on time. WHen you're ready, head over and choose something. Personally, we enjoy Yorkshire Fish & Chips in United Kingdom; Boulangerie Patisserie in France (they have wonderful sandwiches in addition to all the desserts!); either of the Japanese counter services; or Tangierine Cafe in Morocco. There is also Sunshine Seasons in Future World.
Depending on what time you arrive, you could also take your counter service meal and eat it while waiting for Illuminations to begin (since you'll want to grab a seat about an hour before the show starts). It's a great way to soak up the Pixie Dust!