Bibi will remain PM. Avigdor will morph into his pet leftist and do his dirty work for him (Ehud and Tzipi were before him). There will be a big rightist coalition and some Chareidim in the government, but Avigdor will be the leftist whose job it will be to frustrate the right at every turn. This is how Bibi does business.
Sounds like Bibi has learned well from John Boehner, and Mitch McConnell.