Running a 100' of a good quality RG6 coax from the Home Distribution output to your pool room is not a problem whatsoever. You should not worry about any grounding problem nor cable resistance. The coax input on your TV is AC coupled so there won't be any direct contact to the pool room grounding and since the coax output doesn't carry any DC voltage there is no problem with the cable resistance either.
Your only consideration should be the RF attenuation of the coax cable at the UHF frequency for your given length. You can run even a much longer cable with a simple inline amplifier. As far as the UHF remote, use the setup below and you will be fine (you don't need the attenuator in the drawing).
Your only consideration should be the RF attenuation of the coax cable at the UHF frequency for your given length. You can run even a much longer cable with a simple inline amplifier. As far as the UHF remote, use the setup below and you will be fine (you don't need the attenuator in the drawing).