I had the same problem with the Y and was never able to get beyond it. A letter from my Sensei, in English, explaining what 3dan meant in aikido, what training I had received, and his personal recommendation that I be able to teach was not good enough. I also supplied a copy of my dan certification and links to the aikikai website, but that still wasn't good enough.
Apparently what they wanted was more of a certification from a nationally recognized organization, more akin to a physical trainer certification. It was all very frustrating because they actually had someone renting space to teach a Tae Kwon Do class! Probably because they saw that more as a competitive sport than a martial art.
However, I think this is case by case. Someone else a few cities over is having no problems with their Y, and another person is teaching at a community sports center and not having any problems.
Good luck to you!
France doesn't have this problem since they have actual governing bodies for martial arts. In the US, without a governing body, anyone can certify anyone else. Like it or not, that is the way it is.
I have my own organization, I have an LLC to protect me. I have my published standards and we have a board of directors etc. So, I am more than comfortable cutting certificates for people that I think are qualified to teach in a "Y". Of course, you run the risk of liability and getting sucked into a suit...hence why it is important to have a LLC, board, standards, rules etc. Not that any of that is necessary. The "Y" wouldn't know who to ask anyway, unless the have published standards that say you must be affiliated with AAU, USAF, ITF, or any number of self professed "organizations".
Yoga is a good one and they have the business of Yoga figured out. RYT, and other credentials. the fact is you can be a certified yoga instructor in very little time! and that is good enough for them.
I require my "instructors" to meet organizational standards, we have a instructor training course, and they must be red cross certified in first aid and CPR.
However, YMMV, and yes, you can still simply get your buddy to certify you with a piece of paper. too easy.