I have been painting for a long time and the weather should never create orange peel... If the painter used the appropriate reducer there would not have been a problem. If by weather they meant it was hot and the clear flashed to quick then they needed a slower reducer. So the weather thing makes no sense to me...
If you never wet-sanded and buffed before I would be careful with that. You could easily destroy a fresh paint job if you don't know what your doing.....
Watch lots of video's on youtube and go to a paint supplier and get some advise from them on what compounds to use... And what kind of pads to use with them...

Good luck... Post some pics if you can....