The PAT01 does not have to be on the same circuit as the SR227 receptacles in the pool electrical box.
The X10 RF commands from the PHR03 have to reach the PAT01 and the converted X10 commands to the power lines have to reach the SR227 modules.
You may want to move the PAT01 around the house. To see if you can find a location where the PHR03 can reach the PAT01 and its power line commands reach the SR227 module at the pool.
You may want to determine if the house has a X10 phase coupler in it?
Homes usually have a split 220 volt AC feed. Half the house is on one Line and Neutral and the other half on the other Line and Neutral. X10 power line commands have a difficult time getting from one Line to the other. A passive phase coupler, preferably a repeater coupler will get the X10 power line commands between the Lines.
Many of the new electronic devices will make power line noise and effect X10 commands or absorb {Signal Sucker} the signals so they don't reach the intended module.
If the pool electrical box is metal and probably water resistant. X10 RF will probably not get to the PAT01.
How far away is the pool from where you would like to use the remote?
Sounds like we may need to help you get the PAT01 in a better location to receive the PHR03 and then have the PAT01 power line signals reach the SR227 modules in the pool enclosure. After you try the PAT01 in different locations tests.
Jeff has a great set of X10 Troubleshooting Tutorials you may want to look at.
http://jvde.us/x10_troubleshooting.htm