A. or "The family is letting us stay at their cottage"
The other one makes no sense in proper grammar
During a soliloquy, the character is just vocally presenting his thoughts without regard to the audience. The characters are basically talking to themselves. In an aside, the character wants to talk to the audience and is aware of it.
Here some examples I’d like to go to the beach. I hope to go on a cruise. I want to go to Canada. I’d love to go to Disney
He overcome his problem by building windmills
