I think you are best of assuming the absolute worse.
He is going to leave you while he tries out her on a more permanent basis.
He is then going to divorce you and marry her after denying it until the cows come home.
He is way ahead of you in the what's next game, time to catch up.
So battle stations:
Keep shtum
Make an appointment with a couple of lawyers. Ask for recommendations.
While waiting for appointments:
Find all legal and financial docs
Mortgage, salaries, pensions etc
Get yours and kids passports and birth certificates
Keep these all out of the house somewhere he doesn't have access
Get legal advice
Decide what you want in terms of child sharing. Minimum for him is likely to be every other weekend, one mid week night. Your kids are old enough for this. Possibly 1/2 the holidays. Work out what will suit you and your job. If you don't have one start looking.
Decide what is acceptable in terms of the house.
Then when you have armed yourself tell him how it's going to be. Take back the control and power.
IME coming back from cheating is nigh on impossible. But you can do all the other stuff even if your not sure.
The pick me dance is a guaranteed waste of time and a total humiliation.