Wow, tough one. Here's my three cents.
1) Probably not a good idea to tell any coach (let alone an irate one) to learn the rules. He absolutely didn't know the rule in this case, but telling him that (especially the way you did) just puts gas on the fire. Kind of like telling my wife to "relax" when she really gets upset.
Either find a better way to communicate with coaches, or simply ignore the comment and move on.
2) The coach deserved the first T without question. But I think your partner was right about moving away from the coach. Start walking to your partner to tell him what you have. If the coach is going to get the second T, you should make him earn it by following you or by screaming. He probably didn't deserve to get tossed for saying "Go ahead". Your reaction is understandable in such a heated situation, but that's exactly why it may help to physically move yourself away from the confrontation.
3) Your partner let you down by not attempting to diffuse the situation. He should've been attempting to create a buffer between the two of you. Maybe it all happened too fast for him to do that, but a good partner will try not to let his partner call both T's on a coach. We always say in pre-game, if I give him one, you better give the second one. That way it doesn't look personal.
Sounds like a really rotten experience. But don't let it keep you away. Learn from it. You'll be better.