What is the ruling of Islamic law regarding demanding financial support from the husband for the past nine years and relinquishing custody of the daughter, while allowing him visitation rights, knowing that he abandoned his wife and daughter with her family for nine years without providing financial support or inquiring about them? And is it better to resolve the matter through mutual understanding or by resorting to the courts?

The wife has the right to demand past maintenance if she was not disobedient (nashiz), and she has the right to reclaim what she spent on her daughter if she did not intend it as a donation. There is no blame on the wife for giving her husband the choice between paying the obligatory maintenance or waiving his right to the custody of the daughter if it legally devolved upon him, and it is preferable that this be done through mutual understanding.