It looks as this prognosis was not completely right... :))
The general Force idea is the same as in previous episodes. Every member of Skywalker family is in his personal choice between light and dark side. This internal division is inevitable due to the way Anakin was created. All his descendants genetically face the same fate and temptation to the Dark Side.
Anyway this female is not a child of Han and Leia. She is a clone of Leia, created by using a genetic material taken during Lea’s arrest on first Death Star. It survived the explosion and later was searched and found by some of the Empire high ranking officers. They created the clone after it became clear Leia is also a Jedi, so the clone could become a new leader, helped by the power of the Dark Side.
There is no another Dark Side lord or mentor for the clone. The leader of Empire survivors is not a Sith, he is more a political figure and some kind of loved step-father for her. Kylo Ren is the real leader of the awakening Dark force and the new Empire cause. Anyway after reaching high level of Dark Side knowledge, Kylo is creating some kind of Dark Side order. He(She) is believing the limitation of Siths to be only 2 was the weakness that led to their defeat. And on opposite – the big number of Jedi-order members helped them survive after “Order 66”, and hide from the Emperor and Vader. So this mistake will not be repeated and Dark Side army will be greater in number.