Get your own bank account right away. Start protecting your assets and prepare for the divorce. Just because you prepare for it, doesnt mean it will happen. Separate all financial matters. Do not move out of the house. Do not let her take the kids out of state until an arrangement is made. If she gets upset, so what! She is having an affair with another man! She doesnt care about your feelings in all of this, so dont worry about hers.
See a lawyer, get the ball rolling. Make sure she understands that you will not settle for anything less than shared custody of the children. They can stay with you and visit at her place.
please protect yourself. If this affair continues, she will be spending your money to have a good time with his broke butt.