Now, if I remove the white and black wires from the relay and cross them the gate and/or garage will operate depending on which ones I cross. So, the relay seems to be working, the remote control works by itself, but when I tell it to operate by clicking the buttons on my iPhone (while everything is plugged in) the relay activates but the gate/door does not.
A circuit diagram would help
Not sure what you mean by 'cross them'.
Do you mean you cross-them over to the other relay contact or did you mean that you connected them together.
If you connected them together (briefly) I am guessing that this simulates pressing a button on the remote control.
If this is the case, then it does not, as you say, prove that 'the relay seems to be working'.
To me it suggests the opposite - that the relays are not making (closing) the contacts.
If the leds you refer to are on the relay board, then i would look at two things:
1. are the relays themselves working, as opposed to the leds on the relay control circuit
With the black/white wires removed from the relays, use a multimeter to check that the relay contacts actually close
2. If the relays have change-over contacts are you using the correct pair of contacts
It's hard to make out what the relay board is from the image, but it looks like a sainsmart module.
I haven't used one, but looking here http://www.sainsmart.com/sainsmart-uno- ... jects.html
(scroll down the page to see a close-up) it looks as though the common connection on the relay is not the centre connection. To get the two wires (black & white) connected when the relay turns on, it looks like you need to use the outside two screw connectors on each block of three. The centre connector is 'normally on' with respect to the common connection.
If the relays are not working, do you have sufficient power to drive them
Where are power and ground connected - are they connected to pins on the Pi's header or are they connected to a separate power source.