OP - I'm so sorry you're going through this, and your daughters as well. I can't imagine how gut wrenching and surreal this must be for you.
Be gentle with yourself. It's very easy to say LTB when looking in from the outside. Your world has been flipped upside down, and it would be extremely normal to have a whole bundle of very mixed emotions at every stage of this. Sounds like you've loved the man you thought you'd married and share children with, faithfully and selflessly for many years. That won't all go away over night, however, you've just found out nothing was what you thought it was - your marriage, and your husband. You've suffered a tremendous loss, so be very kind and gentle with yourself, and make sure your needs are met so you can be there for your daughters.
If you feel overwhelmed, break it down. You only need to get through 5 minutes at a time, and please, please, please, be selfish through this. Put yourself and your daughters first.
If it were me, I'd be seeing a man who's proven himself to be very comfortable lying to get what he wants - right up until yesterday morning in his text message. If it were me, I wouldn't ever be able to trust him. And you owe the OW nothing! This is sick, twisted bahaviour from both of them, even just the bits you now know.
As someone who's been through cancer (pregnant when diagnosed), is childless, and now dealing with infertility, I can promise you it wouldn't have made me this much of a dick! To anyone! I still put the people I love in their rightful place in my life and treated them with respect and consideration. And I'll always be sure to protect my relationship as my top priority, as long as he does the same.
You deserve so much more respect, honesty, trust, and love. Whatever you choose from this point on, the dust will settle, and children adapt, especially if they're watching a strong, kind, loving and happy mum flourish.
You only ever need to get through today!!
Thinking of you and your daughters x