I have had my 05 MDX for 2 months now and it has been broken into twice

I spoke to the dealer in SF and they mentioned thieves can use a lock picking tool to unlock your car door. Supposedly this is a huge problem in my area. The part I have a problem with is the way the alarm is set up once you unlock the door through the key hole it turns off the alam (I confirmed this with the dealer, the chip in the key only prevents the engine from starting with a fake key not the door). I understand that cars are going to get broken into regardless of what you do, but the fact that my alarm isn't even going off is a joke. Are there any fixes other than an aftermarket alarm system someone can think of? Anyway to program the alarm to go off anytime you unlock it through the key hole even if it is the correct key?