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I would thank her for her reply, courteously and briefly point out her errors, and then ask the following (modify as applicable to you):
"I am concerned, as are you, for childrens' safety, and especially my childrens' safety. That is one of the reasons I obtained a CHL: to be able to protect my children from people who would do them harm. I would ask what you have done to protect the children in your facility from harm. While I understand your concern over an accident occuring with a CHL-holder's weapon, the same can be said for law enforcement officers' handguns, which you do not prohibit. At the same time, there is a chance that there will be a situation at your facility that would require armed response to protect the children. You have taken away that protection from the children in this facility (by their parents or other CHL-holding adults). If you are going to follow this direction, I would strongly recommend that you utilize metal detectors at the doors (as signs have been shown to have absolutely no effect on deterring murderer's intentions) and armed guards to provide the necessary response for when the criminal enters around or through the metal detector. (Note that metal detectors do not prohibit the carrying of a weapon into the facility, they just give you an earlier warning.) Otherwise, you have created an unsafe condition for the very children you are trying to protect. I would hate to be responsible for creating a situation that resulted in the death of innocent children. I'm sure you would too.

Thank you for your time and careful consideration of this matter."

I'd save the issue of the walk to/from the facility for another day. Just thought that this might have an infintesimal chance of getting the wheels turning in her head. Talk to the issue from her standpoint. What do y'all think?