I like how you handled it. While I wold have contested the person asking me to leave and asked to see policy, I think you handled it well. If I'm packing, I'm not disarming for anyone. If their policy is to not allow any for of carry, I won't shop there or I will at least keep it hidden. If that target would have gotten robbed after you'd put up your sidearm, you'd have felt pretty silly and helpless.
Frankly, I only think someone is a potential criminal when they react in such a mannor. If they think I'm up to no good, I assume they have the potential to be up to no good as well or they wouldn't have thought it in the first place. However, I guess that may be irrational. I grew up around guns, so I've never though "hey, this is a good tool for a crime" I've always seen it for what it is, a means for protecting myself from the criminal.
Anyhow, you did great and at least you didn't make her first experience one of those"look at my constitution" deals. Potentially, they got a letter and now she's educated on it. If not, I'd take your letter from corporate to that place and make sure you give the mgr a copy. Its for their own protection, I can't see why they would want anything otherwise. Its like constant free unndercover police patrolling their store.