How will the 7 Kingdoms react if Tommen & Myrcella die before Stannis?

[Peach King]

Nope. 

[Vaith]

I don't think Cersei taking power is completely out of the question. We have seen widows taking charge in inheritance disputes before, like Donella Manderly/Hornwood, and Barbrey Ryswell/Dustin has been ruling Barrowton for quite some time. However, there is a difference between the the Iron Throne and relatively smaller northern lordships. 

If Tommen and Myrcella dropped dead "right now" (i.e. let's say Varys's crossbow gets them after the ADWD epilogue, with Cersei still waiting for her trial), the small council would probably lead a great council, considering either pardoning Stannis, legitimising Edric, or perhaps (as there seem to be no more descendants of Rhaelle Targaryen), considering the claims of Doran Martell, Selwyn Tarth, Lord Plumm... or, due to Tarly and Tyrell being on the council, perhaps even Daenerys or Aegon?

But going off my own gut feeling and reading other theories, I think they will only die once Aegon has taken the throne. Then Cersei will likely escape and declare herself queen of a court-in-exile (because she ironically talked about relocating the court to Casterly Rock in AFFC...) before her fated eath.