Praise be to Allah.
The divorce issued by one who is angry and does not know what he is saying because of his anger or temper does not count as such. But if his anger did not affect his reasoning, and he knew what he was saying, then it does count as a divorce. The issue of divorce at times of anger has been discussed in the answers to questions no. 45174 and 22034.
The husband has the right to take his wife back and it is not essential that she agree to that, so long as he is taking her back within the ‘iddah of a first or second talaaq, because Allaah says (interpretation of the meaning):
“And divorced women shall wait (as regards their marriage) for three menstrual periods, and it is not lawful for them to conceal what Allaah has created in their wombs, if they believe in Allaah and the Last Day. And their husbands have the better right to take them back in that period, if they wish for reconciliation. And they (women) have rights (over their husbands as regards living expenses) similar (to those of their husbands) over them (as regards obedience and respect) to what is reasonable, but men have a degree (of responsibility) over them. And Allaah is All-Mighty, All-Wise”
This verse points to the conditions of taking back the wife, which are:
1-That it applies to talaaq (divorce). If it is the matter of annulment of the marriage, the husband cannot take her back, because Allaah says “And divorced women”.
2-That it should be a revocable divorce, which can only be a first or second talaaq. The phrase “The divorce is twice” [al-Baqarah 2:229] refers to the divorce where it is possible to take back the wife. If the third talaaq takes place, then he cannot take her back unless she marries another husband in a genuine marriage, then he separates from her in a proper manner after consummating the marriage.
3-It should be within the ‘iddah period, because Allaah says “And their husbands have the better right to take them back in that period” i.e., during the ‘iddah. If the ‘iddah comes to an end and he wants to take her back, that is only possible with a new marriage contract and mahr.
4-By taking her back, he should not intend to harm her, rather he should intend to reconcile and set things straight, because Allaah says “if they wish for reconciliation”. If he intended to harm her, she has to prove that to the shar’i judge so that he may rule as he sees fit.
The verse clearly indicates that the wife has no choice in the matter if the husband wants to take her back, and she has no right to refuse to go back to him, because Allaah says “And their husbands have the better right to take them back”. Even if she does not go back to his house, if he says he takes her back and brings witnesses to that, then he has in fact taken her back.
The ‘iddah period during which the husband can take back the wife is “three menstrual periods” i.e., three menstrual cycles according to the majority of scholars, or before she gives birth, if she is pregnant.
Based on this, what is mentioned in the question about him wanting to take her back after two weeks is within the ‘iddah period, unless she was pregnant and gave birth before he took her back.
Divorce does not take place just by keeping away from one's spouse and forsaking her. In the answer to question no. 11681 we have explained that a lengthy absence on the husband’s part does not count as a divorce unless a divorce is issued by the husband or qaadi.
The husband who has several wives must fear Allaah with regard to his wives and treat them fairly as enjoined by Allaah. For more information on the obligation to treat co-wives fairly, see the answer to question no. 10091 and 13740.
If a man forsakes his wife for no legitimate reason, that is haraam. If he shuns her in order to set her straight and make her do some duty that she has forsaken or give up some sin that she is doing, it is permissible for him to forsake her.
Undoubtedly for a man to forsake his wife for such a long time (a year) indicates that the problem is serious and that they cannot solve it. In that case Allaah has enjoined appointing two arbitrators, one from his family and the other from hers, to examine the matter and rule according to whatever they think is in the interests of the couple and will ward off harm from the one who is being harmed.
Allaah says (interpretation of the meaning):
“If you fear a breach between them twain (the man and his wife), appoint (two) arbitrators, one from his family and the other from hers; if they both wish for peace, Allaah will cause their reconciliation. Indeed Allaah is Ever All‑Knower, Well‑Acquainted with all things”
The husband should understand that he is enjoined to do one of two things:
He should either keep his wife and treat her kindly, or he should divorce her in a proper manner, giving her her rights and not wronging her. Allaah says (interpretation of the meaning):
“after that, either you retain her on reasonable terms or release her with kindness”
And Allaah knows best.