This isn't about controlling her at all. You are setting a boundary for you that is healthy. You aren't telling her that she can't have a cellphone. You are telling her that you won't be paying for a cellphone to enable her to continue her affair as that isn't something you are comfortable with. I would look into changing plans and putting your children on your plan or paying the portion of the bill that is your children and telling her to come up with the rest. Standing up for yourself when it is necessary even when it makes someone else mad has to be done. Holding in repressed anger and resentment will get you nowhere. If you pay that bill you will end up angry at her and angry at yourself for letting her have control of your emotions.
"It is excruciating pain. It is the pain of separation, the pain of loss, the pain of dreams and expectations unrealized. It is the loss and death of a mirage."