The Right Way,
When my sons were in high school, a very intense Yeshiva, I approached the Menahel with this exact question – should I ask my sons, or pressure my sons to learn during Bein Hazmanim? His answer was a very quick and emphatic, “No.”
He termed it as a Yeridah Shehi L’Tzorech Aliya, and told me not to pressure them at all. Whatever they do on their own is great, but I should not pressure them, and C”V, never display any outward displeasure if they don’t learn what I, personally, would have liked to see from them.
They rarely cracked a Sefer during Bein Hazmanim in High School!!
Now they are all in upper Beis Medrash, and when they’re home for Bein Hazmanim they all learn pretty intensely every day – without a word from Tatti.