A rough calculation is this. If a full timer works 40 hours a week (5 x 8 hours) and gets 22 days holidays plus 8 bank holidays that's a total of 30 holidays. That equates to 240 hours a year.
If your mum works 12 hours a week she is entitled to 12/40ths of 240 hours= 72 hours.
From this she takes 8 bank holidays @ 3 hrs= 24 hours. And she takes 2 weeks at Christmas but as that includes 3 bank holidays she really only takes 7 more days at Christmas- and that's another 21 hours.
So that leaves 72-(24+21) = 27 hours.
Which at 3 hours a day means 9 days.
Spot on!