If you fail at stealing the ring, you’ll have to obtain some more lockpicks from a Trader to keep trying or simply level up your Speech skills. Once you have the ring, sneak back out of the house and head to Rattay Mill. Close the door behind you to avoid being heard by Hermann. Do this without being seen by him or his dogs.
If you are unsuccessful at convincing him to leave, then you’ll just have to sneak into the house. If you are successful, he’ll leave for a good amount of time and you can steal the ring with no problems as long as you’re skilled at lockpicking. First, try talking to the Executioner and select the option Try and get him out of the house.