Not sure but think late January may be best price wise over February. We've gone late Jan. & mornings started off cool ( light jacket, pants ) but by noon we were in shorts & tshirts. Kids swam during afternoon too and just wrapped up in a towel real quick or pulled on sweats as soon as they got out of water.
Seem to remember some good deals around this time ( late Jan. ) on cash CRO reservations at
DVC resorts ( think SSR & OKW this year ).
As pp said check into AS Music family suite or cabins at Ft. Wilderness resort might be good choice ( these have full kitchen & bbq on deck ). They can probably eliminate DDP by having breakfast, lunch & maybe some dinners as well at suite or cabin. They can save by not renting a car & utilizing WDW transportation (especially Magical Express to/from airport) In addition to being an adventure in itself ( fishing, boating, petting zoo, hayride, and free evening campfire w/ Chip & Dale + movie <this is free to guests staying at any wdw resort too> ) Ft. Wilderness Resort may offer them better options to get to parks & other resorts as well ( boat goes to MK where they can then hop boat or monorail to TTC or to CR, PR, GF; and they can boat or walk to WL too ).
For a moderate resort I second POR Alligator Bayou rooms sleep 5 (but they could find it bit of tight squeeze). They'd have food court at both Riverside & French Quarter ( they are easy walk to/from each other or they can boat it )and there's boat to DTD to Wolfgang Puck Express & Earl of Sandwich; they are good value/substantial portions and work well for dinner (McD's there as well).
Value resorts can be really fun & even more savings for accommodations but they'd need to take 2 connecting rooms. Definitely do not rule this option out because it could still be good deal pricewise and would give them advantage of kids being in their own room and a second bathroom. A code if it becomes available can make 2 rooms at a value extremely attractive.
No Park Hopper option is definitely a savings for tickets. Just need to plan well which park on which day to take advantage of extra magic hours offered. If they take some 'off' days from parks they can save some money as well although usually if you are buying tickets for 4 days or more it is very close in price to 7+ ticket. mousesavers.com has a list of fun freebies & inexpensive things to do on property on non-park days.
Cheaptickets.com is excellent to price airfares both direct & with stops.