The wifi should work anywhere around the house, but, the Sky box will have to be connected to the school dish via the cables. That's the only way that the Sky box can get a signal from the dish. Then, the Sky box needs to be attached to the TV. Sounds like you'll need to get someone in to move/extend the cables to the other side of the room. If you have Sky Q, then set up might be different, I've no clue.
Sky Anywhere is a service that allows you to watch Sky tv anywhere, via mobile, tablet and laptop. Not TV.
I think I have that right, if not, I'm sure someone will be along to correct me.