I think the basic facts need restating:
This student has parents who earn too much for her to get fully funded.
Her parents agreed that the sensible way to assist her through uni was to pay her rent, and allow her to use her earnings from previous work and her loan for her living expenses.
The arrangement was thus that she could choose how to spend the loan and savings, safe in the knowledge that the rent was covered.
She chose to spend £120 of her own money on a tattoo to cover up self-harm scars from a time when she was diagnosed with a mental illness.
Her parents hate the tattoo so much they are now saying they are reneging on the agreement to pay her rent and she cannot come home for Christmas. The only way they will allow her back in their lives and to resume financial help is if she has the tattoo removed via laser treatment, at her own expense.
In short: her parents agreed to pay the money the state assumes they will, when calculating entitlement to student finance. This student chose to budget her money so she could afford a tattoo to cover up scarring, and her parents flipped out so much they are now refusing to help with the money previously agreed.
I think offering practical advice on a way out of this jam is really helpful. Shrieking hysterical tripe over her absolute entitled brattishness because she chose a tattoo for her own body, and happened to suffer mental illness as an adolescent, not so much.