How do I repair a broken garage door opener arm bracket?
You might be missing the point.  

Most people have only ever pushed buttons and never actually lifted a garage door, so it's easy hold the belief that a garage door is a massive 200 pound behemoth that can only possibly be opened with a burly machine.   That's absolutely untrue. 

Garage doors are balanced by their springs.  Opening forces are only a few pounds.   When a power opener lifts a door, it's more like walking an old lady across the street.   At least when things are working.

Before openers, if a garage door was having problems, you'd know it immediately because you'd feel it bind, and you'd fix it early.   Now that we push buttons, the lifter just muscles the door through the defect, which of course does nothing to improve the situation.  Eventually the lifter stalls, the lifting arm breaks, or the door tears itself apart.  That last case is super bad:  Since doors amount to a spring balanced against gravity, doors contain lethal amounts of energy at all times. If a door fails, it can kill you.  

So when a lifting arm breaks, that's your deity looking out for you.  Think of a weak lifting arm like a fuse that protects your wiring, or like the spillway that protects the dam.  You don't want to defeat that.  

Fix your door.

Something is binding seriously in the door.  The door is trammed due to a broken lifting cable, a spring has broken, rollers are off their track or seriously damaged, etc.  Focus on that.