Well the only possibility I can think of is perhaps the timing is a bit skewed. What version of RPi are you using? RPi 2 or RPi 1?
I am a bit surprised that RFToy cannot detect the signal sent from RPi — even if the timing is a bit skewed, it should still be able to pick it up. To make sure I am on the same page: assume the transmitter is connected to pin 15, when you send a signal, do you hear the relay noise? I understand that it made a noise when your RF transmitter is not connected to that pin, my question is when the transmitter is connected to pin 15, does the relay make the noise? This is a indication that the controller is actually sending signals out. If not, that means the controller does not recognize the code and is not sending the signal out.
If it is indeed sending signal out, ideally RFtoy should be able to pick up that signal and shows the decoded hex code. You can compare it with the original code and find out how much the timing (last four bytes of the hex code) differ.