A doghouse ( or kennel) is a small shed, often built in the shape of a little house, in which a dog is kept or can run into for shelter from the elements.
The expression "in the doghouse" means to be in trouble; often used of a husband who is figuratively sent to the doghouse in the same way that a dog is removed from the human habitation. The disdained person may also be "sent to Coventry".
