You're married to a surgeon?
Good luck.
Every surgeon I ever worked with in 30 years of Nursing, with 1 exception, had an ego the size of New Jersey. His " I know more than the counselor" makes sense now. Surgeons think they know more than God.
You say you know he's not having an affair...don't be so sure. You'd be amazed at the things that go on at a hospital and the places where people do them.
Get a job. Right now. Not after the summer. Now. You need to be able to support yourself, you need something in your life besides being Donna Reed.
Then do this: You are a mother with children to protect, so you have to protect them. To protect them, you need to plan ahead.
Get a handle on your finances. Make copies of the last few income tax returns, make copies of all your savings accounts, retirement vehicles, tax bills (car and property), household bills etc. You need to have a pretty darn good idea of where your money is and what it is being used for. Keep these copies in a place other than your home. If you have to rent a safety deposit box at a local bank, then do so. If you have a friend you can trust to hold onto these items for you and stay quiet, then save yourself the cost of the safety deposit box.
Next open a bank account in your name only. Make sure that there is a notation on it that your husband DOES NOT have access to it. If the same trustworthy friend is willing to, it would be better to have the bank account in their name, because in the event that you do divorce, if it's not in your name, it's not your money.

At the very least, your name only, no access for husband. Every few days put some money into it...small increments so he won't notice. One good way to do it is to get cash back at the grocery store. Your bill comes to $50, get $50 cash back. The entry shows up as $100 at the grocery store when one looks at the bank statement. That extra $50 goes into your savings account. Same thing like with buying the kids clothes. You take a certain amount, buy the kids what they need, any left over goes into your savings account.
I had a co-worker years ago who planned to leave her unfaithful husband. She had a couple of children, one of whom had medical issues and he had really good health insurance and she didn't want to take the chance of losing the good coverage for him, so she stayed for a couple of years. During that time, she actually squirreled money and savings bonds away in her mother's name. The nice thing about savings bonds is that once they mature, they are actually worth more than what you paid for them. At the very least, they are worth what you paid for them. By the time she actually left him, she had enough squirreled away to build herself a nice little house in Florida.
Watch your credit cards. Make sure he's not spending tons of money on someone else. If necessary, put some kind of warning thing on your credit so it can't be tampered with too easily. Keep an eye on your credit reports...make sure he's not opening other accounts in your name.
Get anything with sentimental value out of your house. Now obviously he is going to notice if Grandma's china cabinet is missing

but he might not notice Grandma's ring that she left you when she died is missing, unless he makes it a habit to look in your jewelry box. And I don't mean only things of monetary and sentimental value. I mean anything of sentimental value. If you have family photos that are precious to you, make copies of them, put them back wherever you keep that kind of stuff and keep the originals in your safety deposit box. I know one hates to think like this, but I have known people in divorce situations who have had 30 minutes by court order to go through their house and collect whatever personal items they might want. Divorce, if you get to that point, can be ugly.