Beautiful bookcase!
Since the joint seems to be sound, I think I would consider NOT repairing the missing chuck of wood. Consider it part of the patina. A gentile cleaning, touchup, waxing and call it done.
What does your daughter think?
As you indicated in your post, repairing it will not be easy and could be disasterous (broken glass, more wood damage, etc.)
I think the least risky repair option is carving a piece to replace the missing chunk. Not easy, but you can start the process without doing any modification to the damaged area. If you decide the replacement piece will match the grain and look good, then you can clean up the edges of the gap to make the patch fit perfectly.
TonyC