Might help if you list what kind of vehicle so others with the same thing can chime in.
Who installed the alternator originally? I assume it wasn't you. Sounds like a poor installation job, and although I haven't heard of it happening, I'm sure if they misaligned some bolts or torqued down the bolts with an impact wrench it could have weakened the bracket. The alt wasn't too heavy, that's ridiculous. it could have been misaligned though, hence the bracket breaking.
As for the a/c not blowing cold, that can happen if you get belt slip. How was your voltage while you had the alternator installed? If you don't have a self-adjusting tensioner on the belt it's normal for a new belt to stretch a little bit after a couple hundred miles and you need to adjust it. Singer alts. also typically have a smaller pulley and you need to use a slightly shorter-than-stock belt. Or it could just be that the shop that installed it accidentally did something to the a/c system to release the refrigerant.
I think the shop that fixed it wasn't' being completely honest with you, but I don't blame them for not wanting to reinstall something that (in their view) might break again. They don't want to have to warranty aftermarket stuff. I also have the feeling like the original shop (or whoever) that installed it might have not done the best job, but that's just speculation.