Putin is Trump's main opponent, so Trump won't let him be the leader. This is a "business".
If you call that a business then be aware about the dirty games being a traditional activities in politics.
They will always compromise their integrities of good services for selfishness interests.
So as you said, if it's a business then they can always put their differences aside and get on that junk as colleagues in the main time while their goals are achieved.
So don't get it twisted because the both chef's are seriously cooking what we don't know what will be served for breakfast.