There is very clearly no glass in the train window when Lucy is outside on the horse.
Viv says the train didn't stop where Lucy was waiting because it doesn't stop at that location on Sundays or Holidays. However, earlier in the episode, the boys referenced the fact that they would be visiting the White House on Saturday, which means they would likely have been traveling the Friday beforehand. Since no federal holidays fall on a Friday (other than occasionally Christmas, which it clearly isn't), the train should have stopped.
When the house is first getting slammed by the door, it's obvious that it's not made of sugar cubes. And in the last shot of the door-slamming, suddenly there's a pile of broken and solid sugar cubes on the floor.
The boys talk about sleeping and eating breakfast on the train from Danfield to Washington, DC. Although Danfield is a fictional place, it is shown in previous episodes know that it's located close enough to New York City to take the train to Manhattan. Based on this approximate location, a train ride to Washington, DC would only take between four and six hours, depending on the number of stops it makes.