1. You shall have to understand law in its proper perspective. There are few grounds acceptable by law based on which you can seek the decree of divorce like cruelty which you shall have to prove with evidence. In your case she might be able to submit some evidence of your having affair with that lady. Moreover, you can not give her the divorce, it is the Court which will issue the decree of divorce being satisfied with your submission of evidence in support of your allegation against her about cruelty. If you can prove that you have had no relationship with the said lady and your wife's allegation is completely false for which you have lost your job, then you can consider it as an act of cruelty on the part of your wife based on which you can file the divorce suit against her.
2. You can live separately from her.
3. you can not live with any one of opposite s*x during the pendency of your marriage and if you are caught living with that lady, then your wife will get evidence in support of your cruel action on her rather that your proving the charge of cruelty against her.
4. you have married in Arya Samaj and have got two kids. Your marriage is perfectly valid as per law.
5. Mother is the natural guardian of her children up to their 5 years of age.You can file an application praying for your custody of the children for their welfare which you shall have to establish with evidence.
6. Your wife can not take any action against her for your having the alleged affair with her.
7. It the management has is satisfied that she has done misconduct as per the Service Conduct Rule of the organisation then certainly she can be terminated. Normally management asks the person to resin and in case of refusal, the Management takes steps to ease her out or create such a situation that she is compelled to resign.