Assuming you find some alternative chemical to eliminate the particular target weeds, I suggest you evaluate the relative risks of those vs. roundup (or generic). When you have a feel for what you would do if it were your field, try and have a conversation with her and educate her as best you can.
Your approach of giving her the options and costs of each, is a good idea. I would just add the education and guidance aspect.
Even no chemicals and just cultivation and discing has a negative impact. You use more diesel, time, soil compaction. And remember, not all weed seeds will germinate at once. Every time you disturb the soil, some of seeds that were present before will germinate. It could take several cycles to match chemical treatment. You would have to turn the soil, disc, let things sprout; do it again, and so on. It would take weeks so you would probably loose a growing season. So the efficacy is questionable... or at least the efficiency is.