"Determines"

The meaning of "carve out" in this sentence is "shape / form /determine". So, "the choices made by parents shape / determine their children's future"

Thanks so much

As much as I agree with both answers, I think something is missing. The idea of "carve out" is a sculptor creating a statue out of stone or wood. Alternately, it can mean cutting a path through thick jungle, but the original idea of "carve" is still about cutting into something hard and solid - ie. making a path is difficult, as if the jungle were solid rock.