Is the door of repentance open for a sinner who commits sins and breaks an oath, and are the marital problems he faces and his deprivation from his daughters a punishment or a trial from Allah?

The door to repentance is open as long as a person has not reached the death rattle (ghargara) or the sun has not risen from the west. Allah accepts repentance no matter how great or repeated the sin may be; rather, He rejoices in it and transforms bad deeds into good ones. The conditions for repentance are: abandoning the sin, regretting it, and resolving not to return to it, along with concealment and not publicizing it. Repentance must be immediate. If there were unexpiated broken oaths, expiation is required for them. As for the calamities that befall a servant, they may be a punishment or a trial, but the servant should review his relationship with Allah, for no affliction descends except due to a sin, and no affliction is removed except through repentance. One must review oneself, renew repentance from all sins, be diligent in performing obligatory duties, avoid disobedience, and frequently engage in ذكر (remembrance of Allah) and supplication.