How to overcome difficult sections
Many a music student just practise a difficult section over and over again and just hope that at some stage the muscular memory will be trained enough to go through the section without too much of an accident.
Practising both hands separately may be helpful, but many people find it very difficult to co-ordinate both hands afterwards.
For some people it is actually difficult to not play all the notes and they would rather sacrifice every other aspect of a section of music, like rhythm, basic pulse, mood and phrase structure than not trying to have all the notes.
In serious music theory there is a man named Schenker who developed a form of analyzing a piece of music which went from very basic to more complex every step pulling in more details of the actual score.
You can compare it with building a house. Do the builders try to wall paper the walls immediately whilst building them and perhaps even fitting in the nails for things to hang up on the wall? No, of course they will not.
Schenker analysis may go something like this:
C (6 bars) G (10 bars) :: G (8 bars) C (8 bars) :[
This is useful information for the aspiring piano performer. It is good to be aware of what is the key of a certain section you are working on.
Once you have familiarized yourselves with the phrase structure of the right hand, perhaps leaving out ornaments you can gradually 'pull in' the left hand, first playing the bass notes on the first beat of the bar and gradually filling in more until you can play both hands, without impeding on other important musical aspects. At every stage you are practising the essence of the music.