You're not alone. We don't value what we do with our kids, because a whole huge segment of society doesn't value it either. We use phrases like "just a mom" and "I don't work" and "I'm not part of the real world." We don't see the skills it takes to do what we do.
We also don't accept that we are multi-dimensional beings and we can enjoy aspects of life at home, life in an office, life with our mates (without kids) and so on.
You don't know what you would do if you had free time? So find out! Have your husband take the kids and you stay home but do not, do not, DO NOT do laundry, dishes or housework. Read, watch TV, do your nails, paint a canvas, stencil a wall, sew a dress, anything you never do. Or, have him keep the kids and you leave, with a do-not-return-before time. Go to lunch (with a friend or a book - both are fun), go browse in a furniture store or clothing store, take yourself to a movie your husband doesn't want to see (be daring and sneak in a sandwich that someone else made for you at the sandwich shop), take a class at the home center or craft store, go to an art gallery or museum (yes, just you!), or sit on a beach or in a park. The only rule is that nothing you do can be for anyone else's benefit. No shopping for groceries, no reading a book about being a better organized parent, no "I'll just pick up the dry cleaning while I'm out," no checking on the sales for kids' clothing, no calling to see how everyone is or answering calls to referee a fight between the kids. No one calls you unless someone is in the ER or on fire. Period.
Find yourself. It might take more than one trip. That's okay!!
When you get home, you will find at least one of several things. Maybe it was a disaster, the kids fought, Dad couldn't find anything or make the right lunch, they missed you, it looks like a bomb was dropped, etc. Which means you are not a non-person - you run a good home, you keep on top of everyone's needs and wishes and favorites, and your husband has relied on your extensively. Maybe no one appreciated you as much as they should. Maybe this is a wake-up call for them. Maybe it's one for you.
Or, while you're out, you will come across other people in various lines of work. You may get a sense of other jobs you could do or wouldn't dream of doing. You will figure out that you can be alone with yourself, find some things to enjoy, find other things you don't want to repeat. and just BE something besides at someone else's beck and call. You will have taught your family that you are person with needs, wants, wishes, desires, and interests.
It also means you are good at scheduling, dealing with complaining "customers", balancing a checkbook, stocking a kitchen, waiting tables, remembering that there's a washing machine going at the same time there is a casserole in the oven, answering phones, handling emergencies (real and otherwise) and listening. Those are good job skills. If you don't get a call back from an application you filled out, that does not diminish your value. Maybe it's the company. Maybe it's their needs at this time vs. your skills.
I took 2 days a month when my son was little - weekdays, not weekends when things were crowded, but you do what you can. My husband worked at home and my son napped 3 hours a day. So I took him to preschool, and then kept on going. My husband picked him up, gave him lunch, played or read a book, put him down for a nap and went back to work but was there whenever he woke up. My son learned wonderful things about the love of a hands-on father, he learned that 2 people can give baths and grocery shop and play blocks and settle him down for a nap. He learned that my life did not entirely revolve around him. I learned that I was not defined by mommy rules but that being a mom was something I enjoyed but not 24/7.
Try it!