S has the right to decide what she wants out of life. You can't debate a person into becoming who you want them to be.
She also does have a point about time issues. A person only has so much time, and if she thinks it would bother her to try to be poly and have to split up the time, then it's probably not for her.
She's also got to wonder, even if things did work out now timewise since D is far away, what would happen if you moved to where D lives or she moved back? If you moved, then S would have to deal with a long distance relationship. If D moved, then S would have to split up her time with you. If she's mono, then she'd have a lot of time to fill where she'd be missing you.