I have a vintage teak dining table that I bought for a very pretty penny. I also have two young children. FWIW, I keep covering the table with different vinyl tablecloths (once they wear our, etc). You just wipe it after every meal and done. If you decide to go that route, make sure that the tablecloth has a good soft backing so as not to scratch the table & prevent heat damage.

I order my tablecloths from a retailer in Quebec, Canada, because they have good, non-cheesy, kind of more European "look" selection.

Virtually all table tops have water resistant finishes. Water Resistant does not mean water-proof. Remove the glassware from the top when done with a meal. Water is not as much a problem as alcohol and heat damage. Most "Water-damaged" tops are caused by people having a party and leaving their beer bottles/mixed drinks on the table top for hours, or until clean up the next morning. That alcohol attacks the finish. The other issue and far more prevalent is heat damage. A hot coffee cup on a wood table surface for fifteen minutes will do far more damage than a hundred water glasses. Always have something under a hot object on a wood tabletop, and it needs to be more substantial than something thin like a tablecloth.

A good quality vinyl tablecloth (with soft, thick backing) will definitely help with the heat damage. I also use placemats on top of the tablecloth; and of course, if I set down a hot serving dish, I'd put either a trivet or a wood cutting board under. Just use common sense :).

I raised 2 kids and had very frequent visits from 7 grand kids....and all tables are wood! A matter of fact, when I inherited my mother's mahagony diningroom table I gave my antique walnut one to my daughter with 4 kids and she used it as her everyday kitchen dinner table.
Placemats at every meal and coasters for glasses. Clean up spills promptly and a coat of paste wax every 6 months. Hot dishes go on a trivet or hot pad. Kids really need to learn to take care of nice things.

Look for a Formica topped table. Or get a good pad and use vinyl tablecloths.

When our kids were growing up we had a custom made solid surface table with wood base. It worked perfectly!

If you don't want to use a tablecloth because you want to see the wood table, and if you don't want to use placemats because you think they look grandma-ish, then get a distressed table. But you still need to use trivets and such if you plan on putting hot dishes on the table (unless you don't mind burn marks). Some distressed tables are gorgeous - it's just your attitude about it.

I have a horror of formica tables....and glass "to protect....and plastic table cloths.
I keep a silver plated trivet on my dining room table and that gets a hot dish, when I take a hot dish to the family room table ( an antique round oak table) I slide the potholder I used to carry it under the dish.
I guess it's what you grew up with....our kitchen table as a kid was maple.....and not stained. My grandmother had oil cloth tacked to the top of hers.....and it always looked awful!

Yes, you are wrong to assume that a good/decent wood table can take moisture or heat without damage. Not sure what you mean by a distressed table, but even a distressed finish will will show white marks from heat and moisture.

Maybe a quartz tulip table? Although I don't know how it stands up to stains.

My mother's basement kitchen has her original chrome and Formica set from the 50's. Still looks great.

I think, too, if you avoid using really wet cloths to clean up after the kids, or if you do, wipe it dry right away. I'm not sure you could find one that's distressed, but maybe look at a maple table. It's a really hard wood and is usually lighter in color so doesn't as easily show water marks or get dings.

https://www.amishtables.com/blogs/athome/93620609-choosing-the-right-wood-for-your-furniture

Placemats, nothing grandma about them. Put them down at mealtime and pick them up when it's over. When my kids were little I had a variety of kids placemats for them. It made it fun for them and hopefully taught them not to put items on bare wood at other people's homes. Years later we still use placements and the table still looks fabulous.