Hi Claire,
I'm so sorry you are dealing with this very serious situation with your mother. Somehow you need to convince her that radiation will not do any harm, does not hurt, won't make anything worse but in fact will improve her quality of life. The idea is to treat the pain caused by bone mets and keep it from getting worse, and perhaps even slow the process of deterioration. Let her know it's not an aggressive treatment, and causes no pain at all. The worst side effect is fatigue but that doesn't always happen (and it might be dose dependent, I'm not sure), and palliative radiation as opposed to curative would have less of an impact, would be lower dosage and less treatments.
Tell your mother that since the doctors are recommending this treatment so heavily you allowed them to set up the appointments. Then it will be her choice whether or not to actually show up, but get the appointments booked in any case, it might be easier to get her there that way. Ask her to at least try one or two treatments and if she find it awful in some way then at least she has been given the actual choice to go or not.
I wish you and your mother all the best,
Wendy