i dont see the point in sending them to a private nursery if you dont require childcare? Plus I doubt any nursery would let you register for only 15hrs of 'free' preschool time. Our nursery just gives lump sums each term time so you get the hours free that way but your monthly bill is just the same.
It's not for "childcare" - it's early education.
Early education entitlement can be taken in a variety of settings - and one of those settings are private nurseries. Some nurseries are registered to provide early education entitlement, and some are not. Those that do register to provide do so with the local council, and so are funded for this. So a nursery that provides early years education WILL let you register for only 15 hours of free pre-school time.
The fact that it is provided in a private nursery is irrelevant. They all follow the same education programme as a nursery attached to a school.