If Botswana invades, kills Mugabe and his main confederates, then leaves, they will be savings millions of lives, and very potentially returning a nation to its recently-passed prosperity (they were the breadbasket of sub-Saharan Africa for years). I say give them equipment, supplies, training, and positive support in the global media and the UN. Invade away!!
Unlikely.
The Botswana Defense Force (http://en.wikipedia.org/wiki/Botswana_Defence_Force) is considerably smaller and more lightly armed than the Zimbabwe National Army (http://en.wikipedia.org/wiki/Zimbabwe_National_Army).
Nice thought though.