I was asking to see if I could find you a better rate with a company that does permit spouses to drive for free. Unfortunately, it appears that Stanford does not permit alumni to utilize the university's Hertz contract for leisure use. But you might want to reach out to Stanford's purchasing or travel office and double-check. Stanford Alumni Association members have access to Avis and Budget discounts, but I'm not sure how good they are at Lihue. (I cannot view the codes; I am not a member of the Stanford Alumni Association.)

I did not attend Stanford, but my (East Coast) alma mater does permit alumni to utilize its contract rates for personal travel. The Avis and Budget discounts on Kauai were not great, but the Hertz rate seemed to be pretty good:

For pickup and drop off at LIH Airport:




I saw an even better deal with the alma mater rate for pickup at the Hertz Lihue HLE location (about three miles from the airport), with a return to LIH Airport:



Although you cannot use my alma mater's rates, perhaps you can find a good Hertz rate for which you do qualify; and then consider picking up the car at the HLE instead of at the airport.

(I did notice that some rate codes do not permit a one-way from the HLE to the airport.)

Good luck!