I do remember something like this with older Hondas when I was installing alarms and remote starters. You can use a valet key for the remote start since the car will only be "running" and not moving.
When you remote start your car it only needs the chip in the key to be near the cars ignition to override the OEM immobilizer system. You should not drive with that key as it for valet use as you have found out.
They lock and un-lock so the $3.00 an hr. valet that works for tips does not lock your keys in your car.
Just so you know when you open you car with the non-valet key and put it in the ignition and turn it to the "on" position will override the valet key and its limited functions. If its like most remote starter system the car will shut off if you hit the brake and try and put the car in drive without "A real" key in the ignition and turned to the "on" position.
Good luck with your install and let us know how everything works our.
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