Put a second Freesat dish on the second TV and make sure you have at least a Dual LNB fitted to the dish (or buy a quad LNB and don't use 2 of the outputs) Fitting type for the LNB depends on what dish you are using at the moment.
Forget about the antenna to the bedroom. Use the cable to pull through the second sat cable from the loft where it would connect to the dish LNB.
You're not converting any signal to digital.
Use an old Sky box with an old card, or a standard Freesat receiver for the bedroom.