Islam allows the husband to punish his wife by beating her without harming her. I hit my wife on her hand and her leg few times in one incident; that was the only time I ever used force with her. Now she asks for divorce because I hit her; can she do that?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If a wife does something wrong for which she deserves to be disciplined and then a husband beats her lightly without causing any harm to her, she has no right to demand divorce. Asking divorce without any valid reason is not permissible in Islam. The Prophet said in this concern: "If any woman asks her husband for divorce without some strong reason, the odour of Paradise will be forbidden for her". [Reported by four Imams of Books of Sunan] We strongly advise both the husband and wife to be kind and patient with each other. Each one should tolerate the other's shortcomings, since conjugal life will not be free from some troubles and problems. So, one should bear it patiently. If every time a wife or a husband faces some unpleasant event he/she wants to solve it only by divorce, the result would be failure of many marriages, loss of children and destruction of society.
Allah knows best.