The best way to avoid legal issues with someone you're dating while married is to not date anyone else while your divorce is underway. Any activity that appears to be intended to stop your spouse from finding out about your dating life should be avoided at all costs. As previously said, the only method to end a marriage is through divorce.
If you are a member of the military and you date someone other than your spouse while your divorce is underway or even after you have "legally separated," you risk facing criminal charges.