How do I fix a broken window in my aluminum framed sunroom?
I'd replace just the sheet of glass, which can be obtained cheap/easy/quickly at nearly any hardware store or similar.  The store will cut a piece to your measurements.  

Taking care to not damage anything else, I'd remove the outside bevel, cutting/ripping it out, destroying the bevel if necessary.  By bevel, I mean the triangular piece that normally presses up against the glass.  It looks to be about 1/2 wide. This would not involve drilling out any rivets or using a rivet gun.

I'd then insert a new window pane, then either reinstall the old/new bevel, or just caulk it place with a silicone caulk.

The important thing is to not damage anything else.

For measurements, you can cut a piece of cardboard to size and test it out in the opening. Bring it in to the store to show the employee and to compare it to the piece that they cut, just to double check that it is the right size.