I discovered that Keystone used very cheap splitters and most of the RF connectors were loose. Cheap cable, poor connections, and longer cable runs will result in appreciable loss of signal as you get farther from the source.
In our 5er, the antenna feed enters the booster and then splits (-3 dB) down each leg. The first goes directly to the living room TV. The second leg is again split (-3 dB) to the bedroom and lower garage/cargo area. Given the ~20 ft cable run to the bedroom and various insertion losses, I estimate another -2 to -3 dB loss in signal. This means that I'm receiving about 8x less signal at the bedroom TV than the living room.
I've reconfigured some of the cables and splitters and replaced the original Winegard amplifier with the Sensar Pro signal meter/amplifier and added the Wingman add-on. These mods significantly improved overall reception.
In your case, I'd add a splitter just before the existing amplifier and attach the outside cable to one output and the inside cable to the other. Then add a dedicated amplifier to the outside cable run. This will provide maximum signal to the outside tele.