When my LO was with a childminder, I was lucky that she was small enough that she still fit in her infant carrier. Because she was still under 20lbs, she had to stay rear-facing anyway, so we just provided the carseat to my childminder (who only had a forward-facing one).
For nursery, if they take the kids on a trip, they request the carseat. They've only had one trip since Roo started there (instead of being at the childminder) and it was a day that Roo didn't attend nursery so we didn't have to figure it out. But what we'd probably do is give them my parents' Volvo (Britax) Multi-Tech. At this point, I don't know whether we'd stipulate rear-facing or not, it'd probably depend on the length of the trip as much as anything else.