We bought one last year between our four boys, the controller that comes with it (called a joycon) can be used as one controller and split into two for many games.
A lot of games are for more than one player and you can buy more controllers. Another joycon was about £80 last year, looking in shops last week they were about £60 in some shops. You can buy wired controllers which cost around £20 - £30, more for patterned/special editions.
There are a variety of games suitable for various ages too, and it's portable (we bought a case, you can get screen protectors etc).
If you have one Switch you can connect more than one controller and play multiplayer, if you have two Switches you can connect via the internet to play games together, but you need a game cartridge in both Switches. And considering the games generally cost between £35 and £50 buying two of each will get really expensive if you don't need to buy them, especially if you have already forked out for two consoles. (Which I know you're not going to do anyway, but it's also not cost effective to have two in one house if you don't need two.)
Sometimes as a family we play Mario Cart (2 boys and 2 adults together, sometimes the 4 boys together etc.) We all enjoy it. There are other games to play either as one player or together too.
It is one of the best console purchases we have made, and that is high praise coming from me as we have always been a PlayStation family! (Still have a PS1, PS2, and PS3, but we chose the Switch over the PS4. Sorry Sony, we deserted you for the Switch.)