I hope your spouse makes a swift and complete recovery.
Driving trips are a grey area. The Sapphire Reserve Benefits Guide is here
https://www.chasebenefits.com/sapphirereserve2 , and the description of the Emergency Medical and Dental Benefit begins on page 14.
The Emergency Medical/Dental Coverage provides reimbursement for Emergency Treatment if You become sick or accidentally injured while traveling on a Covered Trip up to two thousand five hundred ($2,500.00) dollars and is subject to a fifty ($50.00) dollar Deductible
The problem is the definition of a Covered Trip:
Covered Trip – arrangements that are made by a commercial licensed
travel establishment consisting of travel agencies and/or common
carrier organizations, for which the expense has been charged to
Your eligible Account and/or rewards programs associated with Your
eligible Account, which is not travel for the purposes of obtaining
medical treatment
However, if you booked the hotel in advance I would file the claim because that probably satisfies the Travel Agency requirement even though no Common Carrier was used.,