I agree you might have difficulty claiming this as redundancy, or at least I don't think it's clear cut. Redundancy is one of the following situations:
the employer has ceased, or intends to cease, to carry on the business for the purposes of which the employee was so employed; or
the employer has ceased, or intends to cease, to carry on the business in the place where the employee was so employed; or
the requirements of the business for employees to carry out work of a particular kind has ceased or diminished or are expected to cease or diminish; or
the requirements of the business for the employees to carry out work of a particular kind, in the place where they were so
employed, has ceased or diminished or are expected to cease or diminish.
If they need to half your hours to 15 a week I think you could claim it as redundancy on the basis of the third reason. If they wanted to keep your hours and pay the same but just change your days, then the third reason is still your best argument on the
basis that the requirement for a daytime nanny has ceased, but it's iffy.
Have a read here about changes to terms and conditions and what happens if you don't agree - you'll see that if there is a genuine business need, they could force through a change to, say, 5 days instead of 3.
In the event of a redundancy situation, you would forfeit your right to redundancy pay if you refused a 'suitable alternative' post. Things like personal circumstances can be valid reasons for saying that a proposed alternative isn't suitable, so it is possible that if your employers chose to handle it as a redundancy, and offered 5 days as a suitable alternative, and you refused saying it wasn't suitable because of your personal circumstances, you could then be entitled to redundancy.
But if I were advising your employer I would be saying depending on whether they wanted to reduce your hours or change them around, they could do it without having to worry about redundancy.