of this husband’s deserting his wife for so long and depriving her of her rights is outright injustice that he is not permitted to commit. If what you have related is accurate and he acted without any Shar‘i justification, then his conduct is unlawful and he is indeed wronging her. He must repent to Allah, restore her rights, and ask her pardon for the injustice he has done. His children likewise have rights over him; he must neither neglect them nor be lax in their upbringing and welfare.
Caring for one’s children is a tremendous responsibility. Even if there is a dispute between him and their mother, that does not relieve him of their rights upon him.
In any event, the matter is a serious one. He may not wrong either his wife or his children; rather, he must repent to Allah and return to what is correct. If he refuses, the case must be referred to the walī al-amr (the competent Muslim authority) so that he can be compelled to comply. Allah, the Exalted, knows best.
Question: Does this wife have the right to claim maintenance for the past two years if she has not waived it?
Answer: Yes, she may demand that maintenance, unless she herself was the cause of its suspension—for example, if she was nāshiz (defiant toward him) or disobeyed him in a matter that is her duty toward him. In such a situation the case needs to be examined and adjudicated from both sides.