Due to insurmountable differences between a man and his wife, if they decide to live separately, without dissolution of marriage, then will the marriage automatically dissolve after a fixed period of time according to the Hanafite school of thought? If yes; then what is that time period? Can they re-establish their relationship after a certain period? If the husband refuses to divorce; what is the Islamic and legal way for the wife to apply for divorce? If the wife takes the divorce, is the husband obliged to give maintenance for children if the children live with his ex-wife?
Imām Abu Hanīfah is of the opinion that if a husband and his wife live separately for a long time, divorce does not come into effect by default. However, he opines that a divorce effectively takes place when a husband does 'Īlā (a practice that was rampant among the Arabs at the advent of Islam whereby a husband swears that he would not maintain sexual relationship with his wife). The Holy Qur'ān has given clear directives in this regard that the husband should not thus drag his wife along and must decide within four months if he wants to reestablish the contract.
So if he does not decide within the stipulated time period about the relationship, then divorce would automatically come into effect. However, the case that you have put forth is entirely different. The husband and wife have decided that they cannot live together, but for some mutual interests, for example, to avoid the disastrous consequences befalling the family, especially children, or for any other reason they mutually decide to live separately. Obviously, this is not a case identical to 'Īlā.
As far as your questions regarding divorce are concerned, you must know that a wife needs to ask her husband first to divorce her if she sincerely feels she cannot live with him anymore. If he does not respond to her request, she has the right to turn to the court of law which can force the husband to free her.
The husband is only obliged to keep his divorced wife in his house and provide her during the period of 'Iddat. If the woman is pregnant, then this responsibility is extended to the day she gives birth to his child. The matter of guardianship will be dealt with according to the circumstances and position of both parties and the agreement they make while separating. If the husband does not hand over the infant to the mother and she sues him, then the court will decide who should be the guardian. There may be cases where it is the mother who bears the burden and still, in some other situations, the father is asked to shoulder the responsibility.