There has been a deep ideological and political differences between former Yemen dictator Saleh and Houthi. Hence, both indeed sidelined each other during the last three years. e.g., Houthi refused to dismantle "revolutionary committee” and Saleh (GPC) sought to dominate the political scene.
Saleh and Houti alliance was merely a marriage of convenience and it was a matter of time for it to break up. Saleh fought the Houthi rebels for six-year (2004-2010) which has transformed the rebel into effective militants that know nothing but war. And when it was convenient Saleh made an alliance with them in the face of the Saudi-led Coalition. But the savvy former president miscalculated the fact that a reckless/populist rebel group with no clear political agenda can make the flammable cocktail and will eventually fire on his face. Saleh death is the result of survival driven erratic policies, now he joins the fate of his predecessors of the Yemen Arab Republic presidents (Former North Yemen) who were either ousted in coup d'état or assassinated.
Anarchy looms in Yemen and today we witness the destruction of what left of the "Saleh-authoritarian" state in Yemen and the rise of a theocratic non-state actor (Houthi),- who strive to rule by creed and sword!