These come in a number of colors, including antique white and grey.

https://www.birchlane.com/--Thaddeus-Solid-Wood-Dining-Chair-X114161698-L168-K~B000604374.html?refid=GX433452955865-B000604374_170984472&device=m&ptid=902330322909&network=g&ireid=96744682&targetid=aud-553280535067:pla-902330322909&PiID%5B%5D=170984472&gclid=EAIaIQobChMIytCYoayc6gIVLwiICR2G1Q6OEAsYDSABEgLnUvD_BwE&piid=172959635

Several colors on this one, also.

https://www.birchlane.com/kitchen-dining/pdp/wyman-upholstered-dining-chair-b000206215.html?piid=1050017902

IMO a mirrored dining table with kids is a lot more of an issue that washing slip covers. As for chaira why not just live with what you have until the kids get a bit older I do not think the chairs shown work at all and a $ 100 chairs will look like a cheap piece. I would do ghost chairs but they will cost more than $100

I don’t know how your home is decorated or what your style and color preferences are, so these are just some general ideas. I would not do ghost chairs here, as they scratch easily (I have one).

This comes in several colors (grays, browns, orange, etc) ...

https://www.houzz.com/products/button-tufted-fabric-dining-chair-azure-prvw-vr~159500932

Brown:

Did go above budget a bit on this one:

https://www.houzz.com/products/vintage-french-upholstered-fabric-dining-side-chair-with-wood-legs-light-gray-prvw-vr~159610398

Sleek and modern, leather, great price:

https://www.houzz.com/products/metal-and-leather-cantilever-style-side-chair-with-chrome-base-set-of-2-gray-prvw-vr~132812220

This is basic, but would be very kid-friendly for now and great price:

https://www.houzz.com/products/contemporary-dining-chair-in-gray-finish-set-of-2-prvw-vr~154251492

These would be very easy to recover in a fun fabric and mix traditional with your sleek glass:

https://www.houzz.com/products/muse-ladderback-chairs-set-of-2-prvw-vr~76219708

Most of these come in other colors if you’re not into gray.