The Crown (Tommen and his council) are losing influence in several of the seven kingdoms. They're still strong in the Stormlands (Baratheon), Westlands (Lannister) and to some degree the Reach (Tyrell) and Riverlands (Which isn't technically one of the seven kingdoms but is a big chunk of land so whatever- the Freys).
The Iron Islands (Greyjoy) and Dorne (Materll) are basically acting now with no regard to the crown.
Littlefinger has positioned himself as the most influential person in the Vale, and now potentially positioning himself with a great deal of influence in the North. Neither is really paying much attention to the crown at this point, and their relative seclusion means that there's not much folks in King's Landing can do about it.
But why would this lead to Littlefinger betraying Sansa and Jon?