What I don't understand, and I mean no disrespect, is two things: (1) why is this a big deal? If she doesn't want to see the LTC, show her the TDL. This is such a small issue I am surprised that it bothers anyone. And (2) why are people showing their LTC as primary ID anyway? Is it a sort of showing off thing or something? What I mean is, unless you're open carrying, why not just show your TDL as a primary form of ID?
The other thing is, why not have a folding ID holder which you keep in your shirt pocket? That's what I use. It has my TDL on one side, and LTC on the other:
http://www.walletgear.com/hardy-double-id-wallet.html
This one is a lot more expensive than the one I have, but it looks the same. I'm sure a little google-fu will get you one cheaper than that.
DO I HAVE TO DO EVERYTHING FOR YOU GUYS? 