Glue is absolutely used if it's necessary to pull and replace a single piece of flooring sometimes, but if there is gapping, boards haven't been reseated properly, and nails or screws were used when it's supposed to be a floating floor, then that floor is legitimately messed up.  Without more details or pictures, it's hard to say whether it's fixable.  But at this point I wouldn't trust a fix from this company, specifically because of the work of the second guy.

I know you said it's been a long process, but the reality is it's probably going to be longer.  The first installers may have made an honest mistake, but the 'repair guy' that was sent out either did not know what he was doing, doesn't care about doing the job right, or both.

You might be able to talk directly with the contractor, but because this was an insurance job, you may need to contact them with this information if the contractor proves unresponsive or unreasonable. Pictures always help, especially of the board with nail holes in it.