Here are some possibilities. You take it to Coach to be sent out for repair- doesn't matter if you bought it at Macy's or not (better off not telling them, as they may waive the fee to send it out for repair). If you want to take it back to Coach, don't tell them you got it from Macy's, say you got it as a gift. If they have the bag in stock in the store, they will most likely do an even exchange for you. OR you can probably take the bag back and get store credit for the lowest value the purse has been sold for.
Only thing i am not sure of is if you take it back to the coach store, they will try to look you up (or the "fake" person you tell them that got you the bag as a gift...if they do this, then you cant do an exchange or store credit). I would 1st got to Macys and try to do an even exchange if they still have the bag and then if they don't defnitely go to Coach to get it repaired. Make sure if you're going to have it sent out for repair that you tell them that you have barely used the bag and the strap broke. If you make it sound like the bag was defective, they will most likely waive the fee- saves you $20!
Let's just say I have a special connection and know the Coach return policies pretttyyyy well