It's my understanding that me and someone else can set each other's Xbox as our Home one to enable us both to play any games that we buy. Is this correct? What happens when one of my children signs in on my Xbox, do they have access to both sets of games or only 1?
Here's my example:
I share my account with my little Bro.
I signed into his Xbox, I set it as Home. (He set his account on mine as Home)
I buy a digital game, his Xbox automatically downloads it as it's the Home. He gets to play it without my account signing in. (Vice Versa if he buys)
When my missus wants to play games I own, I need to be signed in. She gets to play any game my brother owns. Hope this helps clarify it?
Basically, in your case, your "Someone else" should be the person buying the games, and he needs to set your Xbox as his home, so your kids can sign in whatever account to play it, whilst this "someone else" must always sign in to play games he bought.