It is possible to have Sky+ in one room and normal Sky in another, we have that.
It is called multiroom and is 10 pounds a month (plus the cost of the sky+ box which is 99 pounds I think).
My guess is Sky will not accept payment from two different people for the service to one house so you will have to get your father to ask sky to come and fit Sky+.
You will then have to pay him 10 pounds a month.
Once he has seen Sky+ he will probably want one himself.