Create a Trigger Code for this and apply it to the Card itself that has access to the target door. Then on the SSP, create a Trigger that is set to look for any condition of Access Granted on the door you want to unlock, but require the matching Trigger Code you applied to the Card. Point this Trigger to a Macro that sets the door to Unlocked mode. Next create a second Trigger that is set to specifically look for Access Granted: Unlocked on the same door requiring the matching Trigger Code. Point it to another Macro that sets the door mode to Card Only. Now you can switch the door modes of this door with the Card.
For multiple relays, you could easily create another Trigger on top of all this that looks for Reader Mode: Unlocked on the target door, and then point that to another Macro that closes the other relay on your ADA push button.