Welcome to SI, the greatest club nobody wants to join. There are some pinned posts at the top of the forum as well as some with bull's eye icons that we encourage new members to read. The Healing Library is at the top of the page and has a lot of great information, including the list of acronyms that we use.
I'm so sorry that you're here. Infidelity pain is the worst, and it takes years to heal. If you can, IC (individual counseling) with a betrayal trauma specialist can be very helpful for you. Your WH (wayward husband) needs IC to dig into his whys and to become a safe partner. What he told you are excuses and crappy ones at that. He needs to get How to Help Your Spouse Heal From Your Affair by Linda MacDonald. It's a nice blueprint to get him started. Another good book for the two of you is Not Just Friends by Dr. Shirley Glass. If your WH wants to R (reconcile), then he needs to do the major work, and that should include therapy.
For you, please take care of yourself and your children. If you think there's a chance that he's been physical with them, then you will both want to be tested for STDs/STIs because there are some nasty ones out there that can turn to cancer.
If you have trouble with depression or sleeping, speak with your doctor to see if there's anything that you can take. The meds can be helpful in the short-term and you won't necessarily need to be on them for the rest of your life.
He says it's all a mistake
A mistake is forgetting to grab a gallon of milk at the grocery store. He has made deliberate choices to betray you. Also, sending your private time videos to others is illegal, at least where I'm from. It is a huge betrayal.
He has also done something very common for cheaters. He has re-written your marital history and has been bad mouthing you to the APs (affair partners). Right out of the Cheaters Handbook (a mythical book we'll mention that doesn't really exist).
You may wish to go see a lawyer or two to see what D (divorce) would look like for you. Knowlege is power, and having an understanding of what it would look like would give you power. You don't have to decide anything or do anything today, but maybe think about it. We're here to help you out of infidelity, whether it's R or D.
BW M 34years, Dday 1: March 2018, Dday 2: August 2019, D final 2/25/21