As someone who does have to use wheelchair service occasionally, my recommendation is the later flight or stick with the original plan of staying over (and staying at the Grand Hyatt DFW for ease of connections in the morning). If they get through immigration and customs quickly (and I've had it happen), they could try to stand by for the earlier flight, without the stress of "what if I don't make that flight."

That being said, do not underestimate how tiring a long flight can be, especially when one is dealing with a health issue. There's been more than once though when I've gotten to DFW and wished I had a hotel for the night because I felt like my body just couldn't take anymore. The option to get a hotel and continue on the next day may be the best option for them.