My guess is that while your colleague may have spoken freely about her son, she had set her own boundaries about how much she would reveal about his death. What happened at the shop may just have been unfortunate timing. However long ago a bereavement occurred, the bereaved will always have good and bad days especially around anniversaries.
If she had set boundaries, you couldn’t possibly know what they were unless she told you, e.g. I like to remember and talk about my son but I can’t bear to think about the accident itself. If he was in any way culpable she might not want to go near that. I note you say she spoke about him not the accident - so maybe that was one of her boundaries and your question inadvertedly stepped over it.
We all, accidentally, put our foot in it from time to time but her reaction and that of the shop manager seem extreme. It was unfair that you were given no right of reply.
Shops and offices have all kinds of rules and regulations about what must be reported to an area manager or head office. That will include staff conflict if the manager felt the incident was serious enough but HO would have expected him to have tried to resolve it before making a report.
If your colleague had laid it on a bit thick about her distress and mental health then that may may account for what, prima facie, sounds like an over-reaction from the manager. Who knows? There might be some backstory to this that you are not aware of.
Don’t discount the fact that you were the person who took over her job after she left. She may feel some irrational jealousy over that and had been looking for an opportunity to see you gone.
For your own peace of mind, I would ask for a meeting, either with the area manager or someone at head office to discover exactly what was reported and why and to iron out any misunderstanding. Get something in writing and an apology if you think it’s warranted.
You say you will never volunteer again but if you enjoyed what you did, then you are letting that one incident take away the pleasure. Three years is a long time just to turn your back on. There might be other branches you could work out or a different charity altogether.
I think we all know people that we have to tiptoe around because of their past, their mental health, their sensitivites, phobias or plain bad temper but you really mustn’t let one isolated incident impinge on your life to the extent that it appears to be doing.