Two things stand out to me, here.

1. The phrase “Am I not allowed to have friends of the opposite sex?” When you spend more time with her than you do with your spouse & family, then no, you’re not. When you’ve repeatedly voiced your concerns but he still carries on with his hurtful behavior, then no, you’re not. If said friend is not also friendly with you, not supportive of your relationship, then said friend is NOT a friend to your marriage then no, you’re not allowed to have THIS friend of the opposite sex. This is friendship has turned into a marriage killer.

2. Privacy is one thing, secrecy is another. I can respect your privacy, but I will not abide the absolute abuse of my trust with all the signs of secrecy. He’s lost the right to privacy.

I’m concerned that his spending the night at work isn’t totally due to weather. I know that you are, too.

Frankly, I would ask him flat out if she’s worth losing you and breaking up the family, because there is no other alternative. I would definitely consult with a family law attorney, just to see what separation would look like on paper and financial support you could expect (assuming you keep primary custody). Assume the absolute worst has already happened. Gather your support, take care of yourself and your kids.