"So in the short time between two presidents the US' interests have changed from keeping us in the EU, to getting us to make a clean break?"
Apr 22, 2016 - Obama: UK would be 'back of queue' for trade talks if it left EU. Note this is before the referendum(June 23rd 2016) It could also be regarded as direct unwarranted interference in the british referendum by undue American influence, unlike all the false news reports of "reds in the bed"

By contrast Trump makes a pragmatic statement contrasting Trade had Brexit been as promised and trade as would be the reality with the brexit betrayal being proposed.

Note one president offered speculation before the referendum the other commented on the contrasting realities after the referendum.   

A totally different set of circumstances!