That is, it is not about them, it is about their mother needing some time for herself. In addition, wherever the kids go would need to provide a solid and consistent structure. They need this in order to get their bearings. A single parent needs to know and work more than twice as much as a parent of an intact family. Now to the kids.
Teenagers have, very generally, two levels of reactions to an event like the loss of their father.
Without these compassionate limits and expectations they will continue to escalate their testing behaviors. Also, this combination heightens everyone s awareness of the kids' needs. The second level of reaction teens have is how they shrink their worlds. The death of a loved one is overwhelming, thus they must make their world smaller, and thus more manageable. On this level teens reduce their worlds to what is manageable, and often measurable.