Sorry to hear of your ownership woes, having failed on the emissions I would have asked to see a receipt for work done to rectify the issue. A replacement tyre is easy spot to check if it's been replaced. Also the emissions print out would have been available had it passed on the day, there's no delay in providing this.
I would rate the garage online in as many places as you can (Facebook, Google, Autotrader) honestly and move on. They'd knowingly done you wrong and even if they rectify the matter, that won't help the next unsuspecting buyer. Plus your time and effort to get the car back, and most likely will need to leave the car there and would you really want that type of trader working on your car? Luckily it's not massive repairs to put right, I know it's not he point but lesson learnt.