If you already have a cable then why not use it? Use the RF output of your STB to feed to your booster instead of the terrestrial aerial. Then, on your second TV, you'll be able to receive the terrestrial channels AND the cable channel.
Something like this:
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Some models of STB are compatible with conventional infra-red devices - which is why I asked for the model number. There is some more info here:
http://www.redremote.co.uk/