Well, I tried it this morning, and it did work.
Normally I have to walk about 5-6 meters towards the car before I get anything, but this time it worked from the front door. I wasn’t even really out of the door either, I was half in the foyer. I’ll try it again later.
Like I said though, my 2 year old manages to unlock doors, pop the trunk and set off the alarm from inside the house. It should be noted however, that she always has the thing either in her mouth or up against her face, so I’m not sure if that’s a factor or not.