First, let yourself off the hook for binding by machine. I do that on every quilt I make. Sometimes the bindings turn out better than other times. I, too, have hand problems, so the quilts would never be bound if that were the only way to do it. To be honest, they wouldn't get bound by hand even if I had no hand problems! I am one of the worst hand sewers in the world....
I use small binder clips to put the binding around the quilt edges. I tried gluing; the results were not wonderful, but ok. The binder clips are a great alternative to pins because they don't stab me! And they hold the binding in place while I sew.
One of the things that I have discovered is that binding by machine requires constant adjustment of the quilt itself during the process so that your quilt top does not hang to the right or the left of the needle. ****The weight of the quilt pulls the quilt to the side and makes it very difficult to sew a straight line.**** Make sure you have plenty of room on your sewing table to put the weight of the quilt on, and pay attention to maintaining its' presence on the table as you bind.
Mitering the corners takes practice. Make a few square or rectangular place mats for yourself and bind them. Each place mat gives you four chances to practice mitering corners without taking up too much time.
When I cut my first binding, I cut it 3" wide. That helped me get it over both sides. Now I can use a strip as small as 1.75" for binding, but it ain't easy! 2.5" works very well.
Most of the time I sew the binding on the back first, making sure that I can fold the binding over the sew line that creates on the front of the quilt. Then, when I am sewing the binding to the front, I make sure the TOP THREAD matches (or is close to) the color of the binding, and the bobbin thread blends well with the backing. Yes, that means I often have different colors in the top thread and bobbin. It's a little extra work, but the payoff is that my mistakes are not very obvious, which means less re-work!
Good luck, and don't give up!