As long as the YouView box doesn't need a subscription to work it should be fine.
Regards the router, you can't plug two routers into two phone sockets on one line and have them work, however you can plug one router into the other as long as the one being plugged in can be set to work as a wireless access point, depends on the router how easy this is to do! Needs a length of ethernet cable to connect them (or powering adapters).
I have this setup at home, one downstairs one up, kids use the upstairs one and can be cut off if they misbehave!