LOL 7 and 9 year olds????  They should still be playing outside.  That is waaay too young to pick up a lazy habit.  $1000 bucks worth of gaming stuff would be an unhealthy purchase for kids that young IMO.  I guess you would have to go with 2DS's and a bunch of games?  There are certainly better gifts that kids that young would enjoy more.  13 year old = PS4 and 10 games.

$1000 each‽

3DS all around with Pokemon and Animal Crossing

1 PS3 with every Ratchet and Clank game, also Little Big Planet

1 Wii U with extra controllers and the Mario Games and Rayman

I am sure still have a grand or so left so...go nuts filling out libraries.

In a perfect world, I'd tell you to buy them all 3DS XL systems, and one of each next-gen home console. An Xbox One, a Playstation 4, and a Wii U. There's literally no reason for there to be more than one of any home console obviously.

With every kid 13 and under, the Wii U is a must. No kid should grow up without Smash and Mario Kart and games like Super Mario 3D World will help the kids bond in a way that they will only fully appreciate when they are adults and that is a valuable treasure. Definitely get them Disney Infinity OR Skylanders. One ore the other, not both. Sonic Lost World is good and even if you don't think so, they will. I thought Spongebob for GBA was good as a kid. Sonic Lost World would comparably blow their minds. Get the Mario and Luigi Wiimotes. Why? They're cool.

Having a 3DS is also a must, since having their own personal system is something that they will appreciate. Make sure that each of the 3DS's are catered to their tastes. Maybe Animal Crossing for the girls. Mario Kart 7 for all four. That's great for car rides. Pokemon XY are too. Resident Evil: Revelations could be cool for the 13 year old. Super Street Fighter IV 3D is also good for the boys. Both are $20 too so they're on the cheaper side. A Link Between Worlds is great. Ocarina of Time 3D is a must too. A good idea though is to just put $100 of eshop credit on their 3DS's and let them chose games for themselves. Give them that freedom to choose what games they want to play. Have them go all digital too. It's easier to manage for the kids and the father and the kids are growing up with all digital.

Last, give them PS4 or XBO. Either will do. Which ever you can find. That's a factor to keep in mind; availability. Get them Call of Duty. They'll be good for KH3 down the road. Same with FF15. Good for sports games. Good for shooters.

get them a WiiU, 3DSXL for ecah one and maybe a ps360. and a lot of games for ecah system.

3DS XL + Mario Kart 7, Pokémon X/Y & Animal Crossing: New Leaf (don't get Animal crossing for the 13 old though) for each kid seem like a good starting point. I imagine if you ask around at the stores at least one of them will be willing to give you a discount for spending a possible $4000 in their store.

i have no clue which console would be the best but skylanders with some figurines could be a good idea as game for the boys but not 100% sure if 13 is already too old for that or if 7 is too young.

Get them a gaming pc with dual 780 ti's, i7 4930k, 64gbs of ram and a watercooling loop. You could probably get a nice 120hz screen or two as well. And $5 left over for games

not sure if a ps4 is really the right choice for the young boy. yes it has knack but as long as the system is really only for him and not also for the father i would absolutely take the wii u instead. especially with mario kart next year + already some released games like 2d mario, luigi and so on...

Nintendo is your friend.
And get the 13y old boy a vita and a ps360 or next gen if you are able to find one.

Something in me tells me they already have a tablet

yeah or skylanders, lego city undercover, mario in 2d and 3d, luigi, mario kart, kirby, playboy, wii party u, nintendo land, wind waker, donkey kong, sonic lost world, pikmin and so on on wii u