My argument stems from the angle of responsibility. Though it is never the mothers responsibilty to proivde financial support for her children it is her right to opt for that if she can provide for them. For example widowed women with families are either re-married or the Islamic state supports them until that eventuality. What I mean is the responsibility can never be on the mother, even if she has the means and her ex-husband is a money waster drop-out the religious responsibility will always be on him, by not providing for his children he will be getting sin and by the mother providing she will be getting a double reward for doing more than that is required of her. This should answer the concerns of PyariCgudia also.
Furthermore I agree and my initial post should reflect this that both parents should be there, but a bit of common sense suggests more involvement of one parent at certain times are necessary for different gender children.
I also said that the mother should not be kept from he children … she has a 3:1 ratio of greater importance to her children than their father, in the general sense. But when specifics are being talked about yes, there are exceptions that need to be exercised.