(spoilers main) Stark civil war?

Considering that Sansa and LF are planning to take over the North and LDS has Robb´s crown and might try and crown Arya (it´s what Cat wanted before she died anyway), do you think we´ll have Jon-Arya-Sansa conflict for the throne? I know people say there´s no way Arya would turn against Jon but if it´s her mother´s last wish, she might reevaluate. Also, I know people don´t like mentioning the show, but in the show ending it looked to me like the Stark siblings didn´t end up on very good terms with each other.