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.
You have to know that it is an obligation to grow a beard and it is forbidden to shave it, as there are clear evidences about this. The Prophet said: "Grow your beards and trim your mustache." [Muslim] The command of the Prophet means that we are obliged to keep our beard, and whoever does not abide by this command, is disobeying Allaah. Therefore, it is not permissible for you to obey your wife when it entails disobeying Allaah in any matter. You have to inform to your wife that shaving your beard is disobeying the command of the Prophet and that she has to love what Allaah and His Prophet love, and hate what Allaah and His Prophet hate. Indeed, the beauty of a man is in his beard. That's why 'Aa'ishah used to swear: "I swear by Him Who beautified men with beards." So it is not a beauty for a man to shave his beard; rather this is the habit and custom of non-Muslims. In fact, they succeeded in introducing us to this habit and unfortunately many Muslims are not acting according to the Sunnah of their Prophet and followed the ways of the non-Muslims.
Hence, it is not permissible for your wife to refuse to have sexual intercourse with you until you shave your beard. She has to be careful not to imitate the devil who calls the people to disobey Allaah. She also has to be careful of the warning of the Prophet who said: "If a husband calls his wife to bed (to have sexual intercourse with her) and she refuses, and he spends the night angry with her, the angels will curse her until she gets up in the morning." [Al-Bukhari and Muslim]
For more benefit, please refer to Fatwa: 84474.
Finally, we ask Allaah to guide her as He is the Only One Who can do so.
Allaah knows best.