sure, in the interrupt routine, you could just do this instead of serial.print:
byte value;
value = digitalRead(2);
digitalWrite(3,value);
There may be an error with digitalWrite taking value instead of HIGH or LOW. If so, try:
int value;
instead of byte.
That should relay whatever it reads on pin 2 out to pin 3. There will be a delay of course, but as long as the delay is consistent, the transmitter shouldn't care.
If you get a chance to measure that voltage, let me know. We may have to do something in-between to get it all nice and happy.
As a last resort, you could try to figure out which pins on the PT2262 that the buttons are connected to and which pins the address are set for from the circuit. That will tell you what commands are what instead of trying to read the remote output.
You could always go with your original plan to hook the buttons up directly on the remote and control it that way, but I think getting this sorted out will be more useful to you in the long run. I won't be able to mess with it much this weekend, but if you haven't figured it out by Monday, I will grab one of my remote outlets and attempt it myself to see if there are any gotchas.