I'd expect most properties to be ok with giving you diamond benefits if you are there and you say your wife is gold too - they may be able to keep your HH account number but just change the name.
However recently I have found that at UK Hiltons you need to mention all of this *before* they check you in. According to the managers of several Hiltons once they have pressed the check in button on the system it is impossible to modify anything (or they preferred to spend time making excuses instead of trying).
FWIW, what they're telling you is BS. Changing a HH profile on a reservation prior to check in or already checked in is very, very simple. Basically, three clicks and done.