United issued refunds for my tickets today. I thought it was very compassionate and decent of them given that my tickets were non-refundable.
Apparently they accepted my rationale for why I cancelled and asked for refunds instead of rebooking for later dates. I had been planning to attend a job fair in DC, but because my mom's hospitalizaton caused me to miss it, there was no point in my attempting to reschedule the trip. I sent them copies of a letter from the hospital explaining my mom's condition, along with a copy of my registration confirmation for the job fair.
Thankfully my mom is improving and may get out of ICU in the next couple days.