...those mitts are pretty intense. I'm not sure why a vet would be so terrified of getting spiked by a relatively-tame hedgehog.
I don't know enough to know if it's a problem, but from the archives it looks like the reaction happens fairly quickly (within a day of each exposure) if it's going to, so hopefully you rolled the dice and it's fine.
If it were my tiny quillball, I'd count this as a learning experience, call up the vet to yell at them and dispute charges (like, why he gave you double mite treatments, which if not directly harmful, is at least a waste of money), and go to a different vet in the future.
For disinfecting a cage, I've found submerging in hot water for a few minutes works wonders, particularly with a bit of white vinegar. If it can't be submerged, wiping it down with diluted bleach, the rinsing that off, should be sufficient. I don't know why you'd need ivomec specifically.
Arbutus West is close to campus -- corner of 16th & MacDonald. I just wrote up a review of them in the reviews section, but the biggest point is that the owner-vet is totally a geek. His people-skills unnerve some people (check out the yelp reviews), but he's obviously into learning every single thing he possibly can about the creatures under his care (check out the hidden yelp reviews; I really do hate that algorithm). I'd also be surprised if he didn't have the biggest hedgehog-cliental in the city, seeing about 50 a year (I had no idea they were such a popular pet in Vancouver!). Apparently the vets can be a bit hit or miss (he's still building up his team after buying the clinic a few years ago), so ask for Dr. Burstyn in particular.