Also, what kind of repair shop cannot get lugs off with the tools they have? I use my impact to remove lugs, but torque back to spec every time.
A number of years back, when I still had my Mk4 GTI, I bought new summer tires for her online from across the border and had it shipped to a PO box on the other side of the border, then installed, balanced by a local tire shop there.
Next winter, when I went to take the wheels off to put my winter setup on, I couldn't budge any of the lugs. I took it to a local mechanic shop a few blocks from my house. They tried, broke the adapter for their impact wrench and said sorry, can't help you. I was thinking oh crap, they were over torqued and seized - this is not going to end well. At this point, I wasn't about to drive 2.5+ hours back to the original shop that did the job to get them to fix this.
I then took it to a VW dealer and they broke their impact wrench adapter and locknut adapter this time.
Took it to a good wheels/tires shop and they tried the largest impact wrench they had, only managed to get 1 nut off after 1 hour. They said sorry, no go.
All the above shops also tried with breaker bars they had, without any movement.
Went to another mechanic shop next and after waiting 30 minutes, they came back to me and said, sorry, can't help you. They apparently broke their breaker bar?! (that's what they claimed, not sure how...)
At this point, I was thinking I would need to drill the lugs out, which would have sucked huge for all 4 wheels. And while I was out and about, happened to drive by a mechanic shop that services big rigs. I thought, maybe they have bigger tools?
I went in and they were nice enough to at least try to help me, even though they don't normally work on cars. They also tried their biggest impact wrench to no effect. Then they pulled out a massive breaker bar longer than any I've seen before. After a trying for about 30 minutes, they managed to get 2 more nuts off, but couldn't budge any other ones.
By now, pretty much everyone at the shop was gathered around to watch the spectacle and suggesting things to try. They were about to give up when one of the guys says 'wait' and comes back with a hollow steel tube about 10'+ long. He then slid it over the length of their large breaker bar. We then had 3 or 4 grown men hang off the end of the steel tube and pulled as hard as we can. That finally did it and got all the rest of the nuts off. They were super nice and only charged me $50, but I gave them $100 for all their troubles.
After that ordeal, I went out and bought a torque wrench and just do my seasonal wheel swaps myself. And any money I saved from buying tires across the border evaporated and then some because some lazy sod at a tire shop effed up a simple job.
Good luck OP with your situation.