All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The husband's saying to his wife, "I do not want a woman like you" is an indirect pronouncement of divorce and the divorce does not take effect unless the husband intended it as we have already stated in Fataawa 90416 and 90531. If the husband intended divorce by it, then divorce took place. Whether or not the divorce takes place does not depend on whether the wife says the same thing in return.
If the husband did not intend divorce by this indirect divorce, then nothing changes and the marriage bond remains intact, and the fact that the wife wanted divorce does not have any effect because divorce is not in her hands.
So, the couple should continue to have good marital relations and live together in kindness as if nothing happened. They should both be keen on doing whatever leads to the family's stability and not exposing it to trouble and division.
They should both be careful concerning the words of divorce, whether explicit or implicit. Divorce is not the first solution when problems occur between the husband and wife.
For more benefit on how to treat an uncooperative wife or husband, please refer to Fatwa 85402 and 97217.
Allaah Knows best.