I was puzzled as to how she got to the magic number of 15, plus public holidays.
It sounds like she mistakenly believes that all FT employees are entitled 25 days holiday per year plus public holidays. Whilst many employers do grant that, your company evidently doesn't - and you are within the law because the 28 days minimum total holiday that Jan1957 refers to includes the 8 public holidays - you grant 29 in total.
Her 3-day week would, in her view, thus be a 3/5th ratio against the 25. (Wrong)
Secondly she is wrong to believe she gets the full 8 days public holiday entitlement - she only gets a 3/5th ratio.
Finally there is a small technical error in my 1st post - because you grant more than the minimum holiday to FT workers - 29 (21+8) days, whilst the legal minimum is 28.
Therefore you need to provide her with 5.8 times her days per week (3) - which is 17.4 days per annum, not 16.8 days. Otherwise you would be disminating against her as a part-timer.
Either way she got it spectacularly wrong to her advantage. Indeed I have never known an employee who calculated it themselves and got it wrong to calculate it to their disadvantage. BM