This not the case, the data protection of 1998 act covers all business types etc and you can be sued/prosecuted if you are found in breach of the data protection act.
If it was me I would of said to the mother ' I understand this must be a upsetting time for you, but I'am unable to discuss the matter further with you due your daughter being over 18 and due to data protection act of 1998 which I am legally obliged to follow/adhere to.
This is clearly a family matter and for professional reasons I do not wish to involved in this any further.
If you can not respect this or carry on harassing me, then I will have to ask you &/or your daughter to find another stylist'
Then I would of sent it in an email with a link to the data protection act.
In the mothers defence, she is upset, angry and looking for someone to blame. So rather than address her feelings with her daughter she is projecting her emotions & anger on you.
In the meantime I would be seriously reconsidering whether to have either or both of them as clients as the position they both have put you in is not a nice one.