The most effective location for an amplifier is at the antenna. But for sure, it needs to be before the splitter. With 50' of coax between the antenna and preamp, you will loose close to 3 dB of net noise margin compared to what you could have had with the amplifier at the antenna. The CM-341X series amplifiers can be powered via a remotely located power supply with the addition of a PCTMPI1G.
http://www.channelmasterstore.com/Am...p/pctmpi1g.htm
If the problem is only a signal strength issue, yes, the amplifier will help. If you have a signal quality issue, you will amplify the noise and interference as you amplify the signal which won't improve the quality of the signal. You need to try and see.
Often the single factor that will improve signal quality more than any other is, locate the antenna where there are fewer obstructions such as vegetation or buildings.