Noah,
I have done similar repairs (on boat, I worked on boats a lot).
I will advise that - if you can - you get that entire trim piece loose. Then you can clean off the old caulk and straighten the piece without damaging the bedding of the remainder. There is probably damage to the side where the screws ripped out and those areas can be tapped back flat before you try to remount the corner trim.
The other remarks about plugging the old holes was right in line. Any soft wood will do. What I have often done is fill the holes and when the glue has set, then I would come back and trim the plugs.
At least you have a decent neighbor.
Matt_C
