This is not possible. While you can have multiple characters on a service account, you cannot play them simultaneously.
While you can attach multiple service accounts to one Square Enix management account so you can pay them all together, they are separate bills.

And yes if they wanted to play on the PS4, they'd need a PS4 license so other than the trial you'd still need to purchase the game itself on that platform. And since you have two kids, you'd buy it twice.