-- Tell her you will not support her if you are no longer acting as a married couple and that you expect her to find work to pay for her cell phone and anything else she needs.
-- Begin seeking alternate child care now so your wife can work
I would start with these ^^^. Start making a list of your family's finances, and what you're willing to continue to contribute to and what you're not. Absolute Item #1 needs to be her cellphone. Cut it off, and then calmly tell her that you did, and why you did it (see above). If she's like my wife was, she'll have her own within 3-5 hours anyway, but that's okay -- BGPs (Big Girl Panties -- she needs to start putting hers on).
Start becoming comfortable with the phrasing "I have decided that _______." As in "I have decided that I'm no longer willing to financially support your affair. This morning I shut your cellphone service off, so you'll need to get your own, in your name." or "I have decided that I'm no longer willing to lie to cover up your affair."
I understand your fear -- I HAVE BEEN WHERE YOU ARE. My kids were older than yours (then 21, 18, 14 and 11), but I get it. I would tell you that your daughters are the very reason why you need to take a strong, honorable, principled stand here. What advice would you give one of THEM if she came to you 30 years from now, in the exact same situation you're facing now?