Is there a service for companion traveling to help with a medical needs patient?

Here is one such service that is based in the Houston area. (I'm not sure what area of TX your friend needs helps transporting to?)
website: msmedicaltransportation/patient_services.html

Another way to handle this is to hire a caregiver from an in-home caregiving agency and explain that she needs someone who can drive her and her husband in the caregiver's vehicle and spend the night away from home at times. There are many caregivers who do this and it would be a way of not only having transportation but having caregiver assistance with the husband. Of course, your friend would have to pick up the caregiver's mileage as well as hotel and food expenses. Still, this would be worth it to have that extra person there to help with her husband.

Private companies offer a travel transport nurse to assist disabled people on long distance transports usually over 300 miles. Another option is to hire a medically equipped motorhome with a nurse and driver such as offered by the MED Transport Center. They take care of everything.

If he as a disease that has a national organization, contacting them is a good idea as they have volunteer lists and as a big plus have been through whatever the specifics are for that disease. For example, if he has leukemia or other blood diseases, LLS - Leukemia Lymphoma Society has a resource list for just that as they have/do events like Light the Night and LLS Regatta's where they get volunteers from. LLS is divided into regions accross the US.

If he is going to Texas Medical Center in Houston (UTHSC, Baylor, MDAnderson)
each hospital has social services that can get you in touch with resources. TMC is primarily folks coming in from outside of Houston so this is nothing new to them. She also should belong to AAA premium for car issues - about $ 100 a yr.