To make the correction, yes it is her right hand. She is on pain meds and diuretics. She does not use a sling. She has also been through what they call a gamanizing treatment. I dont know much about it.
I'm not a doctor; but, I've known of a lot of people who had undergone Cancer treatments (my sister; both of my parents and numerous friends and relatives).
One of the symptoms that I've seen, especially with Radiation therapy, is Edema, which is a condition that results in an excess of fluid build-up (usually in the extremities i.e. arms, hands, feet and legs) causing excessive and painful swelling.
You don't mention if your mom had Radiation treatments... but, when you mentioned your mom's Cancer and it's location (in the brain) what I thought was that... the fluids from the site of the treated area migrated and trickled downwards. From the head area, the arm(s) and hand(s) would be the likely point of fluid build up.
The picture shows her right hand... but you state that her left hand is the one that is afflicted. Am I correct in concluding that her brain tumor was in the same side of her body as is now the swollen hand?
Anyway, this is only my unprofessional speculation. And, unfortunately, it's true what the medical professionals told you.... this type of Edema is a condition that can't be reversed.
As for drug options, it sounds like she's tried many with unsatisfactory results. Where these drugs prescribed for pain management?
Or, where they prescribed as diuretics in the hope of forcing fluids out of her body via the urinary tract?
Does she use a sling for her arm? Doing so might help to alleviate the pressure and pain of the hand.
Hope this info helps... wishing all the best for your mom.
This picture doesnt look as bad as it really is.