If I bring the receiver from the carport to the family room. About 50feet.

I have a small TV, with only the antenna out fitting in the back. Do you think I could hook
It up to the TV??

Yes, if it is running off 2.4Gghz you should be able to get that amount of run from it. Just make sure that there are not many thick walls (concrete) between the run. Also if you have a wireless network it will sometimes screw with it.