I'm glad your kitten is okay. I thought she might have infectious enteritis, which is deadly and kills kittens and adult cats very quickly, though most adults are vaccinated for this.
Having had experience of home vet visits, I know that they're very expensive. This may be a cause of the cynicism of some members here. It's cheaper and quicker to take a cat to the vet surgery, where they have all the equipment and medication needed. Did this vet charge you? If so, I'd love to know what a vet visit costs these days, as it's been a while since I've thought this wise, so mine usually get shoved into a taxi.
Good luck with the little ones. If something like this happens again, go to your vet straight away. Kittens die quickly if poorly. From my own experience I'd avoid out of hours vets if your vet uses the Vets Now service. But go as soon as the vet opens. Do you have a regular vet? Your kittens are going to need his/her services soon - vaccinations, spaying, worming etc. And be prepared for the cost!!!!