The two tos are unrelated. Any parallel or coordination is illusory.
"To commit someone to something" is an elliptical way of saying "to force someone to commit to something".
If we build our headquarters in Toronto, that commits us to frequent international flights.
The second phrasing is a little more difficult to articulate. Generally, if something is done "to the [nominalization] of X", that means "and had the effect of [verbing] X" or "causing X to experience [nominalization]".
The headquarters was built in New York, to the disappointment of many.
Hence, we could paraphrase your original quote:
If a farmer plants a glysophate-resistant crop, she commits to using that herbicide for the season, probably requiring that she exclude all other herbicides and other weed-control practices.