At The Spro, we have a large, LCD tv attached to the wall. It was placed there by the library.
However, during the rest of the week, it is tuned to either CNN or FoxNews and is 99.9% of the time set to MUTE. Even when people ask if we can turn it up, we can't. We do have closed-captioning running so the need to hear the tv is almost non-existent. We have made exceptions for volume during times of significant news or customer interest, i.e. the US Airways Hudson River Crash or Barack Obama's pre-inaugural speech in Baltimore City, but otherwise, it's silent.
My suggestion is to set hard and fast rules regarding the tv and its' usage. Leave it muted. Our TV is specifically for news and nothing else. Designate certain hours and certain channels for tv use. Do not deviate. Do not allow her to change channels to her desires.
Fox News at a coffee shop????