Childcare for a disabled child

I couldn't find the right place for this, apologies if it's not in the correct section.

I have a client who has several children in paid childcare. One parent works, the other is a carer for one of the children and receives carers element in her UC.

We are currently appealing against a decision not to cover childcare costs in the UC claim at all because the caring parent doesn't work (clearly this is incorrect based on F7013 of the ADM) and I'm confident they will succeed on that one.

The remaining question is whether they can claim childcare element for the disabled child, and that seems less clear. She attends childcare one day a week to allow her carer parent to do things that aren't possible when she's home, like dealing with admin and other things related to the care. Their argument is that the work condition for the carer parent is met, so if they show that the care is necessary to allow the carer parent to perform the caring role, it should be an allowed cost.

The added wrinkle is that the child is home educated - but my understanding is that it's not relevant to UC how the parents choose to educate their children (and she could still need paid childcare during after school hours even if she did go to school).

Does anyone have any more detail than what's in F7 of ADM, or any case law that's relevant? Thank you.