if there is a boy home with a 12 year old sister, a 8 year old sister, a baby brother, and a non jewish housekeeper, is it okay for a random girl to stay in the house?
The 2 sisters provide shemira for the brother and this would technically circumvent the problem of yichud. However, experience has shown that a situation as described could be a potential for disaster. Especially if it is a big house with many rooms, spread out etc..
So before allowing a teenage boy to be alone with a girl and non Jewish housekeeper, someone who knows the boy, the girl, the housekeeper, the sisters – the whole picture – should responsibly determine if the situation is a safe one. This may depend if it is a one time thing for a few hours or an extended period overnight etc.