Seemingly, according to religious law (canonically), the religion doesn't suggest to refer for the divorce directly. In fact, Islam doesn't like divorce and tries to prevent it as far as feasible. (Of course not always, it depends upon the case). Actually in the mentioned case, it could be considered as a treason issue, it could be your right for divorce (to if you be able to prove the issue or even you see a problem in your life. But as far as you can, strive to solve the issue positively, otherwise this is your right to do that.On the other hand, occasionally divorce could be an appropriate way to save the persons … (to take action for the divorce) http://islamquest.net (1))
On the whole, divorce has some conditions.(http://islamquest.net (2)) and likewise (http://islamquest.net (3) ). Anyway, apparently, your marriage still could be considered as a valid marriage if you don't take action to divorce her.
In regard to your last inquiry that inquired if I gave her divorce then what about Dower?
- Initially I should point that we could consider Dower from two
aspect. actually it could has two meanings. One of them is Jahiziah
((الجهیزیه او المهر(الوسائل البیت) which is related to the means of
the home (which is considered as a custom is some places). So, in
the mentioned issue, the husband ought to give them(means) back in
the case that the wife has bought them, otherwise it is not
necessary to give them back.
- Secondly, by paying attention to the other meaning of Dowry or
Dower, which usually is considered as Mehr (and is more famous with
this meaning and name), has some specific conditions. For instance,
If a man divorces his wife before he has sexual intercourse with
her, he should give half of the fixed dower to her. Anyhow, I
recommend you to do more inquiry regarding the mentioned matter and
also see the sources below. Since I don't know how it was complete
for you. Good luck.