Rosey, you know your mum best, but I would proceed with caution. It sounds like a very long flight and there are also the other bits: packing, going to the airport, clearing security, waiting, the flight, possible flight delays, the time change, getting to your brother's house, and then the whole thing to do over, in reverse. If you do go, I'd make sure you get clearance from her doctor and definitely have help for the journey. You mention she has trouble using public toilets. How will your mother manage the toilets on the plane? There really isn't room in those for two people, usually.
You also mention your mother has trouble with wandering. What would happen if she did this in the States, at your brother's? Would he be equipped to deal with this?
I wonder if you can enlist the GP to take some of the burden off you. If you are able to say to your brother, the doctor says she can't travel that far, or cannot fly, or whatever, it makes the doctor the bad guy, not you.
I understand that your brother hasn't seen your mum for a while and probably doesn't understand why this is a bad idea. Having said that, I am with sistermillicent: it's a terrible idea, he's mad to propose it, and he is the one who should get on a plane!