Airbnb – the host wants to reduce the number of rooms, can we get a refund?

My family must stay in an Airbnb house in the next few days. It is three bedrooms and advertised as having room for us alone. We are two adults and two children (one aged five and one year old). It's a long drive to get there.

The host sent a message this morning and said that he was having trouble giving us the whole house and that he wanted to confine us to a single room that they thought would house us. We presume that since this reservation was made a few weeks ago, they have other paying customers because they want the custom. They also say that they will give us a reduced rate, but that's not the issue.

We are currently trying to get a refund and try to stay elsewhere because we would not want to stay there and be locked in one room (especially with a baby who is teething and has trouble getting sleep, and good 4 hours driving to get there and the next day 4 hours), and would not feel particularly comfortable with other people there anyway. But is it feasible with the rules of Airbnb? I admit that I have only briefly looked at their terms of use.