Personally, I would just leave it.
When my twins started nursery at 11 months they didn't drink either milk or water from a cup all day. They waited until I collected them, and then fed all night! A bit tiring for me, but they were just fine.
Eventually they copied the other kids and go the hang of drinking from a sippy cup. I tried so many different cups, but it was the nursery cups they mastered first, and I'm sure it was because they watched the others all day.
If you're happy to give formula, then if have your childminder continue to offer milk, but not stress about whether DD drinks it. If you only want her to have breastmilk, then if have the childminder offer water and then breastfeed when you're together - life is too short to express milk that won't be drunk.
At 10 months, and successfully on solids, I don't think it will hurt to be without milk from 8.30 until 4.30, particularly if you can offer feeds just before and just after. She may well just shift the feeds to 1 - wake up, 2 - 4.30 collection (likely to be a big feed, as hungry/thirsty and to reconnect), 3 - bedtime. So you may not get too many extra night feeds :)
Good luck with settling your DD. It is a big transistion, but your DD will either work out how to take a cup/bottle, or she'll wait for you to come back :)