Well the Wii U can play all the retail released Wii games as well as older games through the virtual console. The digital eshop is a bit awkward to use now that Nintendo isn't supporting the Wii U any more. The Switch does have a ton of older games too and the NES and SNES games that come with the Nintendo Online(I don't know if that's been released in the UAE).
Otherwise it's probably very affordable now. Extra controllers are just Wii Controllers. However the Switch does have a gigantic library with most of the best Wii U games ported to it now and it comes with two controllers when you buy it.

Anyway let's focus on games! Smash would be probably too much for them. You can give it a shot but set the AI level low if you do!
Mario Kart is always a safe bet but the you have Sonic All Star Racing Transformed, and a bunch of LEGO games, Rabbid and Rayman games that are all fine for little kids. The Switch does have Team Sonic Racing but it's not as good but it has Mario Kart, even more LEGO and Rabbids/Rayman games.
Of course you've got the parental controls phone app on Switch too that's very helpful.
Super Mario 3D world on Wii U is a 4 player co-op platformer and that helps a lotif the younger ones are struggling. You can run in and save the day. There's a similar co-op helping feature in Super Mario Galaxy 2 for Wii and Super Mario Odyessy on Switch.
All the Wii Sports games on Wii and Wii U are obviously really simple to learn to play so they should be fine with that.
Avoid Mario Tennis Ultra Smash on Wii U, it's terrible, whereas the Switch Mario Tennis Game is better.
The Yoshi game on Wii U is a better designed game but the Switch Yoshi game (Yosh's Crafted World) has the co-op features to help younger players out.
There are also Art Academy games on Wii U for drawing but I've not tried so I'm clueless as to whether they are good.
The Switch has Nintendo Labo, which is geared towards education in most of it's releases.
Just Dance is on both and kids like to dance.

That was a lot of typing. I am going to stop.

Well, there are some boardgames or tabletops on the Switch, like UNO, Monopoly, or, fittingly enough, Pandemic.

Kids love Minecraft. It's not a party game but you can play split-screen. You'll be amazed how quickly they learn to build stuff.

I know this is going to sound like an extremely stupid question axum but can I set up the switch as a home console and let the kids play with the pro controllers  instead of the portable tablet-like controllers? Are all games playable with just a traditional controller and television-set? I'm afraid of purchasing games that are mandatory tablet.

Soren. Thank you for the amazing suggestions. I'm going to make the purchase tomorrow but thanks to axumblade, I'm considering the switch instead of WiiU. I'm assuming all the games you listed can be played on the switch? 

The UAE just announced the shutdown of all non essential stores... so I'm going to have to do this sooner than I thought

I have a four year old at home and his personal favorites that allow local multiplayer are: Rocket League (PS4), Towerfall (PS4), and Smash Brothers (Switch)

Best of luck through all this. He's only been in quarantine for about a week so I imagine we'll reach your point in a couple more weeks. 

Thanks Tor. Definitely going to fire-up the PSstore. I'd appreciate more split screen suggestions. 

It's looking more and more like we're going to get hit hard in America. Stay safe and stay home. Ironically I feel much safer here in the UAE than I would have if I was currently in Cleveland. And with the spring break incidences... ugh ignorance. I'm kinda relieved I delayed quitting my international job last year.

When I have access to my PS4 again I'll check around for what other PSN games I've got that support split screen or otherwise local multiplayer. He's also a big fan of those Overcooked games but it's not something he's actually played successfully while the other games I listed he's gotten surprisingly decent at. 

I work in academia and my wife is in grade school education so they've been home from work for a while now compared to the rest of the US. I think the numbers are going to get extremely high, but I'm hopeful that most people I know have been taking this seriously. 

Edit: He's also enjoyed LBP4 and Dreams, but I'd go for LBP4 over dreams since it's easier to get his head around a game with more consistent rules and feel. Also I think Dreams doesn't support local multiplayer yet but I might be wrong on that. 

Given their age, I guess it depends on how easy is for them to learn standard gamepad controls...if they have no problem with them, Wii/WiiU is probably the best choice, given that there's tons of games with both standard and motion controls. If gamepads are difficult for them at that age (seen that in few cases in my extended family), something like Kinect is probably better fit.

You can read this very long list of recommendable co-op titles for game nights (online or couch) here:
https://www.reddit.com/r/NintendoSwitch/comments/dlx6od/a_very_long_and_updated_list_of_recommendable/

Should help you on your quest!

I got No Heroes Here from this recommendation list yesterday, and it was a nice online cooperative game.
Shame I was not able to get Overcooked 2 while it was on offer.