Our soil is gravelly loam. There's very little clay in it. My son and I want to experiment with making cob and seed balls...but that requires clay. Where can one buy clay when there's none to be dug up?
If you only need a bit, there is often a layer of clay silt underneath the sand in the water on a shallow lake beach. As a kid, I LOVED diving for it, digging it out, and making mud figurines. Might not be ideal for pottery.
Otherwise - most soil (unless specifically manufactured and cleaned) has SOME clay- even if only 3-5%. For your purposes, you could make a small grizzly - basically a screen on an angle. You dump dryish soil slowly onto it. Stuff that is smaller than the screen (maybe use hardware cloth?) Falls through. The gravel bounces off to the side and makes a pile that can be used for other projects. This would give you maybe 10-20% clay, depending on what percent gravel you had. 20% clay is more than enough to exhibit clay-ey properties.
You can buy bags of bentonite chips or ground bentonite. They are clay, but a special expansive super slime clay. Kids would have fun with bentonite, but it's not really representative of most clay.
I think your kids are still too young, but you can do some great science/math problems with a scale and some different sized sieves (if they are doing algebra already- let me know and I will give you ideas)
I'll back Phil up and recommend potters. The type I've had most luck with are local pottery studios where you can get a membership to rent kiln space and wheel time. They always have 25 lb bags of powdered clay for relatively inexpensive (considering the quality you're getting.) If you want I can ship you a box of dirt from my backyard. It's basically red clay with a little sand mixed in. :)
If you are looking for larger quantities of clay you can probably call landscapers or excavators in your area and get it trucked in by the load. However, there is usually a minimum load. Around here it is 8 yards if I recall right. The last time I had fill brought in I had the option of fill sand or clay and it worked out to about $100 a truck load. That was a while ago though so prices might be higher.
If you get clay dirt trucked in, be ready to spend some quality time breaking it up and preparing it for your needs. I had couple truckloads dumped earlier in the month and in order to make my seedballs I need dry powder. The steps to get there from wet clods are many and there's work involved. On the other hand, I have lots of fireclay for RMH projects and it's already powdered and bagged. I'll probably get a few bags of inexpensive stoneware clay for this reason.