Start gathering your paperwork and finances right now. You may not have made any decisions at the moment, but if you have joint accounts, take his name off or take the money out and open new accounts.
You have children so get any copies of his pay stubs, pension plans, bank accounts, insurance polices for possible future use for child support.
He is a good liar and is now trying to find out what you know and how to spin it. This is why he didn't want to face you immediately, he needs to do some damage control.
He will continue to lie. I personally would want to know what has been going on and the who, what, where, how of it all. It's soul destroying to find out that the person you are with isn't who you thought they were.
It will get worse before it gets better, but you need information before you make decisions. The big red flag is that this woman knows all about you and your family and you know nothing such as if they have children together which could be a factor in your child support if you go that route. For all you know, he may have his name on a house/mortgage with her and other debts you are unaware of.
Change any passwords he knows on your bank, phones, tech.
Find the copies of your children's birth certificates, get copies of the past 3-6 months bills/debts so you can make some financial planning if you end it.
When I confronted my ex after his own daughter saw him with the OW, he spent the day denying and didn't come home as I was unreasonable to accuse him without proof.
My ex lied and told the OW he wasn't even married and I found out the lies and the truths when I sat down with OW's husband and he brought 18 months of their FB messages. She may say she knows all about you, but as a proven liar, who knows what he's told her to be the "truth".
As rough as it is, get as much info that you need to make your decisions. Take care of yourself as you have been dealt a shock.
Hugs to you and yours.