Mr. Radhakrishnan:
Being eligible or having sufficient legal cause for divorce (in this case adultery) is one thing and proving in court is another. Proving in time is yet another. Currently it is taking 4-6 years to get divorce just in family court itself. Its a package of about 4-5 different legal battles (498a, DV, maintenance, custody). Note that laws and judges are mostly on the woman's side regardless of whose mistake. In DV case, she can ask for 9 different interim reliefs including child custody, maintenance, protection orders etc. So if you apply for divorce, you will be looking at a very bad situation. With two daughters and job, it is not at all worth going in that direction.
If you don't want to live with her, you don't need divorce for that. Even if she cheated you, for children's sake, it is worth continuing living together, at least until the kids grow up. You can always leave her later. Another option is to just talk to her and tell her you are not comfortable living in the same household as her, so that you may live separately.
I also agree with Mr. Reddi above that nowadays having s*x with others or romancing with just one other person is quite common. The only difference is that you came to know. There are many husbands who simply don't know. So just tell yourself you are one among them and move on. Who knows, she might still be loving you. But her physical, biological desires beyond her control have driven her to get some momentary physical pleasure with someone. Internally you might be the only person in her heart (usually only the husband is).
Summarily, I strongly suggest you forget about divorce and all the legal crap. It can make your life hell. You may lose child custody and possibly even child access like I do now. Wives give a lot of fight back in these situations. Stay calm, and cool. Don't listen to friends and lawyers who might instigate you to go the legal route. They do it for reasons such as ignorance, fun, greed etc. Also I suggest not to discuss these with your friends or family -- it won't help you in the long run. Better to keep them to yourself, cool down and decide. At least you are the one who is seeking divorce, not her so you are in a position to call the shots. Keep it that way.
Good luck. Stay cool.