switching between 12 volts

Ok, I am a dummy when it comes to electronics. I connect the wires and hope for the best. I recently bought an OPT-7 interior led light kit, but I have a problem. The control box has a third wire that goes to the dome light. This is used to power the led lights when the doors open. I have this connected but the led lights do not come on. I have to have 12 volts coming in on the other(main) side for the led lights to work. Ie the dome light wire is acting as a signal wire to the control box for the led lights. My question is, can I wire a relay with two 12 volt inputs and one 12 volt output? If one is powered, 12 volts goes to the output. If the other leg has 12 volts then that side takes over and sends power to the output. An either/or automatic switch? My thought on this is when the dome light is on, it would send power to the relay and tell the other side to send 12 volts to the main side and power the door open led's. When the dome light is turned off, power would be cut off to the relay, and I want the accessory power to power the regular led lights. The way OPT-7 has it, you have to have constant power going to the main for the lights to turn on when the door opens. The dome light wire is acting like a signal wire, instead of a power wire.



      ^
    to led lights------------------>I
      I
      I
       I-------------------------I
       I          I
dome light in 12v     I          I main power 12v in from accessory or constant if I want the door led's to come on when I open the door.
--------------------->I          I<--------------------
       I          I
       I          I
       I-------------------------I

I think I just figured my own question out. Please tell me if this sounds right. I am going to get two spdt relays. The first will have constant power to 30. The door wire will go to 86 and act as a signal wire. Ground to 85 and then 87 will be my output wire to the led light control box. Now 87A will go to the second relay at 86 and act as a signal wire. I will have an accessory wire, powered when I turn on the truck, go to 30. Ground will be 85 and output will be 87 to the led light control box. 87A will be taped over. Should this work? When the dome light comes on, I should have white light for the led lights. When I turn on the truck, the accessory power would take over and power the led lights like regular. When I turn off the truck and lock the doors, everything should shut off.