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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Hasting things and not taking it easy is the reason of every evil. Therefore, if you had accused her without any evidence, you are wrong and you are obliged to repent. However, she should accept your apologies since you apologised to her. Forgiving is one of the characteristics of the noble and pious people. Therefore, we advise you to endeavour to convince her. In doing so, you should first seek Allaah's Help, then the help of whomever you believe could influence her.
Nonetheless, what you did is not a reason for her to leave her marital home and refuse to share the bed with you; otherwise she is exposed to the Curse of Allaah and being deprived from His Mercy. The Prophet said: "When a man calls his wife to his bed (for intercourse) and she refuses and he spends the night upset with her, the angels keep on cursing her till the morning." [Al-Bukhari and Muslim]
Furthermore, she is not permitted to go to work except with your permission if you already fulfil your obligations towards her, like spending on her and providing her with clothing. If she persists in this condition she is disobedient, in this case you should advise her and appoint rational and pious people from your family and hers to arbitrate between you. Then, if reconciliation takes place, all perfect praise be to Allaah, otherwise if she persists on disobeying you and neglecting you, then you may divorce her.
Allaah Knows best.