Does the TV not have multiple inputs? Ours has two on the back, and one on the left side facing the entertainment center. Merely bring the cable in, use a splitter for the bedroom TV, and take the cable to one of the TV inputs. Take the digital converter to a second input. Then, you just have to change the inputs on the TV remote to change from local to cable.
Seems I have seen a converter that changes a IR remote to UHF. Like this:
http://www.criscros.net/Lrrx_ufh.htm