I love the wishbone chairs but with 4 kids I don't think the woven seat would bode well with the crumbs and spills that go along with kids (I have the same dilemma). You could do the all wood version but have only found that to be $$$ or you could do this Hans Wegner chair which is also similar in style:

I particularly like this with the stools you are planning for.

Good luck!

With the wood of the table and the legs of the counter stools, consider all wood . I like these a lot:

Elsa Bent Wood Dining Chair, Walnut Dark Brown, Set Of 2 · More Info

a few more ideas...

https://www.potterybarn.com/m/products/gale-dining-chair-set-mp/?pkey=cdining-chairs&isx=0.1

https://www.potterybarn.com/m/products/ezri-metal-dining-chair-mp/?pkey=cdining-chairs&isx=0.1

https://www.potterybarn.com/m/products/westan-wood-dining-chair/?pkey=cdining-chairs&isx=0.0&isx=0.0