Is it obligatory for parents to try to bring their son back home after he left it due to problems with his wife, or should they wait for him to return of his own free will, and is his action considered a sin?

The brother's independent housing is not a sin; rather, it is a right for his wife. However, it should not be a cause for filial disobedience ( 'uquq al-walidayn) and severing ties of kinship ( qat' al-rahim). If he abandons his parents and severs his kinship ties without a valid Sharia-compliant reason, then he is sinful. He must be advised to repent and be informed of the virtue of honoring one's parents ( birr al-walidayn) and maintaining kinship ties ( silat al-rahim). He should not be left without advice.