Neither of your two sentences (Let's see what will Her Majesty's say be. Let's see what will be Her Majesty's say.) is acceptable/natural/grammatical in any atmosphere.
I concur that the two sentences may not be natural/acceptable, but I believe that at least one of them is grammatically correct. In the former "Let's wait (for) what will be Her Majesty's decision" I see there's a direct object displacement. What's grammatically wrong in the latter (except for the omission of "for" after "wait")? Thank you again. Sorry for the trouble
There's nothing grammatically wrong with the latter except for the omission of 'for'.
Please note that there's no need to post separate 'thank you' messages. Just click 'Thank' in the bottom left-hand corner of any replies you find helpful.
