Bad babysitting situation with a 15 month old- what could we have done differently?

I was asked to babysit for a 15 month old at a friends house while the parents attended a wedding next door. They decided to have me play with their child for 2 hours before bedtime. They wanted the child to have the run of the house...steps and all. They told me I would have to help her with the steps as she had no idea how to maneuver them (of course) but that she loves to play on them. When they left, I found myself running after the child the whole time as she traversed the house, and I decided to try to keep her off the steps as it was too dangerous. I tried to interest her with food left by her parents for her to eat, toys, and little games, etc etc. It was difficult. However, after she realized her parents were gone, then the trouble really began. Crying, tantrums, the whole bit. And when I tried to block her from stairs or anything I felt was dangerous, she got even more agitated and ran to the other stairs. There were four dogs in the house too, and one of them got freaked out by all this and barked at her which was extremely unnerving. I tried everything to soothe her but to no avail. Finally the grandmother came over and brought her to the wedding. I felt really bad! Later, at 8:30 the parents had a hard time getting her to sleep, it took 45 minutes.Then she woke up again while the parents were at the wedding and the whole drama took place for a second time. I wondered if it would have been better to have her in just a room with me, so that she could play easily and we would not have to deal with stairs or doors. Also I wonder if maybe the parents could have skipped her nap earlier so that she would have slept better. What would have been the best setup for her and I so that this wouldn't have been quite so bad? I certainly understand how she must have felt, with a stranger and in a strange house, but I wonder if there was more we could have done to facilitate her comfort...thanks. I feel really bad about this!