@ellaferris - I do a lot of hand quilting myself and sometimes experience that tired hand fatigue that you're talking about. What works the best for me is by reminding myself to take frequent breaks.
Sometimes I place an ice pack over the sore hand for a few minutes which really helps too. I've heard other seamstresses wear support gloves or even hand splints to bed to help fight hand fatigue.
I don't know what's the perfect solution but I hope you will continue training your alternate hand and try to remember to take several breaks. Every little bit helps! Good luck.