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.
If the situation is truly as you mentioned in the question, then your wife is wrong in many aspects:
1- Attending this course without seeking your permission; this is what we understood from your question. Indeed, it is not permissible for a woman to go out of her husband’s home without his permission as we clarified in Fatwa 83241.
2- Being trained by a non-Mahram man in addition to letting him touch her body; there is no doubt that all this is forbidden.
3- Insisting that what she did is not wrong.
4- Refusing to let you touch her or have sexual intercourse with her. In fact it is not permissible for a wife to refuse if her husband calls her to bed. Abu Hurayrah narrated that 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] Indeed, you did well for being angry over what she did, as being jealous over one’s honour and dignity is among the characteristics of ‘Eemaan (faith). However, we do not advise you to hasten to divorce her; rather, you should continue advising her in a soft and gentle manner. Then, if she repents from this act, you should keep her and accompany her in kindness. However, if she insists on what she is doing, then there is no good for you to keep a woman who is insisting on committing a sin, especially if that sin represents a danger for her dignity.
Finally, it should be noted that a husband should choose a safe place for his wife, and she should avoid circumstances in which she might be abused or sexually harassed by others. It should also be mentioned that both spouses should fulfill the rights of each other as this strengthens the stability of the marital life between them.
For more benefit on the rights of the spouses, please refer to Fatwa 85308.
Allaah Knows best.