There are issues preventing women from working. One direct problem is Indian households have always had a women as 'home makers'. So you have to fight a lot of cultural inertia.
There are also security issues. Indian cities haven't been very safe for women especially for women working at night. Crimes against women are common. Also there lack of affordable places like creche's and day care centers for kids preventing women from working post maternity. Most working women quit jobs for this very reason alone.
Secondly, even if women work. The situation in India is worse enough to make them spend that money on their own selves and their families, than their parents.
But I agree, with you that women must be encouraged to work more.
Well actually I think the ultimate goal is people having to work less. Getting women to work sounds like a solution from your problem description. But the real problem seems to be welfare of the elderly. If another solution (like social insurance) could be found, perhaps women wouldn't need to work. Perhaps even society would restructure itself.
Only 60 years ago it was common in the western world that women had to stay at home to take care of the family and household chores. I don't think it was only feminism that changed that, but also technology. For example washing machines probably saved a lot of time (even a bachelor can wash their own clothes these days). Not sure how widespread access to such technology is in India?