Thank you for your question. It is not true that if a wife walks out of the home, the court will automatically give the daughter and home to the wife. Far from it.
New York State is an "Equitable Distribution
" state. This means that, based on the particular facts of the case, the assets and debts will be divided in a manner that fairly represents the parties contributions to the marriage.
The conduct of the parties, such as "walking out" is not considered by the courts unless the misconduct affects the marital property itself. For example, if one spouse gambles away half the marital assets, the court will usually not divide the remaining assets 50/50.
Child custody is determined based upon the best interests of the child. Walking out does not give a parent any additional rights.
A lot of people think that the courts are friendly toward the mothers
in custody cases, but in actuality they are friendly toward the child's primary caregiver, and usually happens to be the mother. It makes logical sense--if one parent has taken on the role of primary caregiver, it usually benefits the child to not dramatically disrupt that arrangement at the time of a divorce.
I should be clear that because the nuances of every situation are different, this information should not be relied upon as complete or advice without consulting in person with counsel, but as a general rule, property division and custody rights
are not impacted whatsoever by a spouse walking out on the other.