Could tywin have beaten the reynes & tarbecks without the cruelty he displayed?

Depends what you mean by cruelty. Surprise attacks, taking no prisoners on the field? Probably needed to correct the huge decline in the authority of the Lord Paramount. Having all of the Reynes and Tarbecks murdered? Not necessary. 

He could have very easily disinherited both families, and sent the survivors to the Wall and/or the Silent Sisters, without killing hundreds and hundreds of noncombatants.