As soon as one hears big thumps while driving, they should really pull over immediately. If they're mechanically minded, after a quick visual inspection to ensure nothing is obviously loose or about to fall off, they could drive away at reduced speed. However, if one is not mechanically minded and more noise is heard or wobbles felt, it's a really really bad idea to continue to drive as you can't assess if you are risking life and limb. In such cases, it's best to have the car trucked to a workshop close to home.
For those less mechanically minded, roadside membership is ideal to include with your vehicle insurance as it's not a costly add-on and provides road side assistance and free towing. So, consider chalking this as a learning experience.
As for the workshop where you left your car, I would have thought the first thing they would have done (in your presence) was raise the car on a hoist and visually check the rear of the vehicle to confirm all bits are attached nice and tight as they should be (exhaust, shocks, wheel nub/carrier, trailing arms, links, brake calipers, drive shafts, diff, etc). Then by simply rotating the drive shaft by hand and then each wheel by hand, this should have highlighted if there was anything binding up the rotating bits and as a result given them a rather strong hint as to what could be wrong. All this shouldn't have taken them any more than 10 minutes at a leisurely pace. So in my view they should have been able to provide a repair quote.
As is, it all seems very undefined and open ended at the moment.
Simply leaving a car at a workshop for them to start dismantling as part of their diagnosis process before any quote can be given puts you in a rather compromised and less than ideal position should you be unhappy with their estimated repair costs. In these cases, if your unhappy with the repair costs, all you can do is say "no thanks" and pay them for their diagnosis, then have your car trucked away with oily bits on the back seat. Less than ideal which is why it's always a good idea to try and avoid such situations. Sometime, such situations are impossible to avoid because of the nature/type of fault but I don't think this case was one of the impossible ones. A quote should have been forthcoming on the day you rocked up (pun not intended).
If it was me, I'd drop by unannounced and check out what is happening. If things haven't progressed and nothing dismantled, I'd consider trucking the car somewhere else as I feel the situation should have been handled differently.
