Even if it the cooking and cleaning statement were epistemically true, it is not instrumentally rational to tell this to your child if your goal is to have her grow into an independent adult who can support herself, and does not feel bound by the "traditional" gender roles (which are falling out of favor anyway).

Indeed. But why suppose those goals? I would value my daughter's happiness above her being independent and untraditional, in part because the former seems absolute while the latter two seem relational. When there are conflicting goals, all we can discuss are the empirical results of polices, and it's not clear to me that this is a case where accomplishing goals and speaking the truth conflict.