A car remote control generally uses a frequency of 433.92 Mhz or 418 Mhz in the UK and Europe.
The RF carrier will be modulated in some way with a code for the various functions, open, close, alarm etc. On some systems the code will change from operation to operation to stop some little tea-leaf with a scanner from grabbing the code to your nice new Mercedes and taking it for his own nefarious purposes.
So unless you can find the code for the alarm function, you will not be able to duplicate the key alarm.
Presumably the auto manufacturer tries to make this really really hard to do--it's just a small step from replicating the panic to replicating the "alarm off/unlock" signal. So unless the auto maker is totally out to lunch, you'll have to figure out what the codes are, and the codes are likely to roll--that is, they'll be different every time.
I had a neighbor years ago, who had the sensitivity on Mustang too high, thing would go off all the time. Seemed kind of stupid, how would you tell the difference between the many false alarms, and that one time you need to drop everything and rush out to save your car? He did a lot stuff to annoy the neighborhood. Anyway, I tried to think of ways to set it off on a regular interval, like every 10-20 minutes, instead of 3-4 times a night.