As I said I do not know what state you are in Aguila Blanca, but your state, as you said, does have an exception for shooting ranges but it is more restrictive than my state of VA. VAs is listed below:
3. Any regularly enrolled member of a target shooting organization who is at, or going to or from, an established shooting range, provided that the weapons are unloaded and securely wrapped while being transported;
Note: this applies only to concealed carry, open carry is fine. I may pick a few states at random to check, but I expect there is a range exemption for transport of weapons in most states for those otherwise legally able to posses them. Some, like your state may only apply to official ranges and organized events.