I think that could be a fun solution. It's the same as the theory behind the clicker - being able to use a new sound that is not common and habituated away improves the learning curve.
The last stage of knowledge for a dog is the ability to generalize the command to different places and people. While I understand your frustrations, I do want to say that I think a long term training goal would be for your dog to acknowledge and respect the sit, come here, down commands from your father. Those commands can be in English or German or whatever you want, but Jamie needs to have respect for all the members of the pack, not just the one that is above her in her viewpoint!
I would guess that your father might not have been too enthused about being told that he needed to be consistent toward a disobedient dog. Not only do we men have big, fragile egos, but it can also be frustrating to deal with a dog that doesn't sit on the first command and waits for that sit, siT, sIT, SIT. My guess is he'll come around when he sees that Jamie is making progress toward being a good, obedient member of the family.