Suspect she was embarrassed so snapped, I don’t think what she did was that bad, not great, clearly there are better ways to handle it, but not world ending either.
Her sons attitude is very common amongst kids who have a parent who doesn’t work but repeatedly says we can’t afford things.
I recall a conversation with a group of my daughters friends and they couldn’t understand why their mothers didn’t work, none of them were raised with the ideal that staying at home was the way to go, and I do suspect that often a parent who stays at home, is more about the benefit to either one or both parents and less about the benefits to the kids, but some how try to pass it off as being all about benefits to the kids.
Where as the kid only sees the down side, constant “we are skint” and they have no real desire to have their parent constantly there.
Her son is getting to the age that for him the simple logic will be if you wish the nicer things in life get a job, and she should explain to him properly why she can’t, not pass it off, as your mother did, as he should feel lucky as he sees her whenever he wishes or her just snapping. He’s old enough to understand her reasons.