This evening, Amy threw up, despite the syrup—first just a little bit, and then for real. That took matters out of our hands and we decided to take her to hospital. (Which was kind of good, in a way—since she was so uninterested in drinking and would only drink a little bit at a time, Stella would probably have had to wake her up every quarter of an hour or so and coax her to drink a bit more. With an IV, she'll probably get hydrated a lot quicker than that.)
Fortunately, Thomas was so kind as to drive us there again. I waited there with Thomas, Stella, and Amy for a bit, but when it appeared that it could take quite a while (there were about four children there, and one person said he'd been waiting for an hour, and there seemed to be not nearly enough staff on the night shift to handle the volume), I decided to leave since there wasn't really a lot I could do. Stella stayed there, both to check Amy in and to see whether she could stay the night there as well.
I hope they'll both be fine.