I think anytime ive failed an inspection, ive had at least a month to get the issues fixed and reinspected without getting charged the inspection fee again. Small two person shops and big dealerships alike.

I couldn't find any information on the government websites or the NH safc3200 about if mechanics are allowed to double charge for an inspection but it definitely sounds a little less than reasonable considering its a reinspection and not an inspection at a completely new shop.

When it comes to finding new issues with the vehicle, it again sounds odd considering the sequence of events and the time period. However I've had a few vehicles where in a two or three month span, a couple parts failed in a row. It may be beneficial to have a separate shop or group take a look for your peace of mind; who knows if the first shop is doing something underhanded and if theyre doing it to other people too?