I don't mean the ring that you equip, I mean the ring that you get for completing the stage which your friend has in his inventory. Which is what helps you open the door.
Completing the stage gives you a 1-5 cobolt ring AND a quest ring (non equipment) that goes in your inventory. To go back to this stage to turn in adaman raid stones, you need to have this quest ring which recognizes you as a 'friend of cobolt' to get 'cobolt friendship' items.
For the second use of that quest ring, is what you are trying to do, have someone with it open the gate for you, but you friend can't get too close to the gate or it will recognize the whole party (you and your friend) as friends of cobolts who had completed the stage before. So your friend has to open the gate from as far as possible (aka just get close enough for gate to open) then he has to leave the map OR throw the quest ring away and do the whole stage with you.