I feel your pain. I had a brain fart and threaded the hole with the wrong thread once, didnt want to screw together to well. Luckily I just had to grab another handle and install a pin to match the threads I cut.
Glass is easy to drill, I use the 3 fluke Ford carbide drill bits for all my work. They are kind of expensive as I have 1/4, 5/16, .307, and 3/8 but they don't walk. MSC sell them but they want twice as much as some other places.
You still should have the original threads will just need to be cleaned up with tap.
I had the same twist apart and break issue with the 3/8-10 aluminum rod. So I switched to 3/8-16 aluminum for a long time and never broke one. And now most of the time I use 5/16-14 titanium to join handles to forearms if I need to hold the weight down.
Have you got a picture of the type of pin you used that broke?
Quite a few materials have problems maintaining strength when there is nicking or a very small radius. Any material that can be scored and broken on that line are a prime example of this. A lot of composites do not cope very well with sharp corners or sharp root thread profiles.