Its in the interests of the employer to offer some sort of compassionate leave. They are not duty bound to offer compassionate leave but if they do it doesn't have to be paid. If the employee asks to take it as holiday the employer can't refuse.
Under these circumstances compassionate leave can be in the form of a partner needing to take care of the children. All as per ACAS when i called them a few weeks ago as we had a similiar problem. Most employers out of good will allow the day of the death and the day of the funeral and can set out terms of leave ie only allowed for close family at the start of employment.

To echo others she has good grounds for unfair dismissal on what has been said. There may be more to the story or they just need to get rid of someone to save money and they saw this as an opportunity. I would make my intentions very clear to the employer, they obviously won't make any friends but at the very least she needs paying for her notice and as it wasn't down to misconduct or in breach of a contract as no formal contract has been signed so only statutory rights apply she may be entitled so some holiday pay if she hasn't used all her holiday up for this period. A well written letter setting out your intentions and detailing any advice you have sought from CAB etc to show you're serious should be enough hopefully and they may just settle what you are owed if they are reasonable.