on another thread on this forum, there is discussion of the same concepts.
one idea was to have a timing that would know if the garage door was opened first, then the house door. that would indicate the need for a fast timing.
if the house door was opened, then the garage door, say to take out the trash, the sequence would indicate that someone is outside and the timing cycle would be longer.
the PIR in the garage would keep it open.
the problem with all this is that if a thief was fast enough into the garage after you arrived that they would trigger the pir and keep the door open.
another common sensor is a optical interrupter at a low level at the door. typically to prevent the door from closing when a child or thing is in the doorway.
you could tie into that and add that to your sequence.
garage door opens, house door opens, house door closes ( it is assumed the garage is empty of people)
then the light beam is tripped, that would beep in the house.