The Pope may change a law with a new law replacing or contradicting it.
Yes, it's possible, but Pope Benedict said that's not what happened. Secondly, Paul VI's new law is not required under pain of sin, so his law has no binding authority. Quo Primum is binding, under pain of sin, so it's authority outweighs Paul VI's non-authority.
Quo Primum was not a change of the previous laws regarding Mass, in case you didn't notice, but a new one itself just as Paul's was.
Quo Primum did not make a "brand new" missal, but simply took all the various rites (which were essentially the same) which had existed since Apostolic times and made the mass uniform. Anything which Pope St Pius V discarded was non-essential.
Paul VI's missal made substantial changes, most notably to the consecration. And since the consecration is essential and from Christ directly, these changes are substantial, illegal and immoral.