As I understand it, FENSA is a self certification system whereby the installer confirms that their work meets the required standard of installation. In your case, clearly it does not, so I would suggest that you just get the process started ASAP and outline your expectations early, ie that you would prefer an independent check on the workmanship and that you would like an alternative installer to rectify the issues.
I do seem to recall that they may need to allow the original installer the opportunity to rectify his own issues in the first instance, so you would need to clearly outline your reasons for being unhappy to allow that to happen early on.
I should also have added that if you have had another FENSA chap around, ask him to confirm his recommendations in writing and make that part of your claim.
Hope you get it sorted.