Recommended exercises for preparing to bicycle commute
I would see a rehabilitation center or certified trainer for exercise for the shoulder. It does not cost that much for 1 or 2 sessions to get a set of exercises.  You will need some light weights as fly will be an exercise.

I tore a rotator cuff and it was easier for me to ride my mtn as that angle was more comfortable. 

I could ride after about 2 months but I could not really exercise as I could not pull. 

I kind of had a sense of what to do at the gym. I was riding hard after about 6 months and pretty much heeled after a year.

In addition to the gym get on the bike and spin around.  Until you are strong you need to be concerned with a fall.  I can ride one handed safely so that was not an issue with me.