Perhaps by allowing your children to go days (and perhaps weeks, even?) without showering, you are hoping to decrease the odds that you will become a grandparent at an early age. Whatever the rationale behind your decision, it is still gross. By the time a child is in his teens (especially because he is in his teens), he needs to shower at least once a day. Possibly twice.
I don't care if you need to bundle your child up in his comforter and dump him in the bath fully-clothed before he's awake in the morning. Whatever needs to happen, get it done.
Your Friendly Neighborhood ESTJ.