How can I refinish wood chairs so they will stand up to every day use?

You can use a polyurethane sealer on latex paint but not sure it would work on chalk paint. You could try wax on that. Polyurethane comes in gloss or matte.

why not use an oil based colored paint. It can come in a mat satin or high gloss finish but any oil based paints will last a lot longer. The color is your choice

I'd not use chalk paint on chairs that get heavy use. Research mineral fusion paint to see if it's more durable; I haven't used it yet so am unsure. I'd use a satin or gloss spray paint personally. If you do this, lightly sand with fine or extra fine sandpaper, then clean the chairs thoroughly with a degreaser like denatured alcohol, then do careful spraying, taking your time and doing many thin layers, lightly sanding before the final spraying. Finish off with a clear spray sealer if you wish.

You can use poly-acrylic over chalk paint or latex paint and that will help, however I would not recommend chalk paint unless you are going for a chippy shabby look. Chalk paint chips easily and I would never use it on anything I want to look nice or sleek. People will also tell you that you don’t need to prime with chalk paint because it adheres well, but I have found that colors bleed through the paint if you don’t prime it first. It doesn’t happen right away, but is is always horrifying when you see the previous color start to come though something you spent a lot of time on. I don’t use chalk paint anymore.

To get the best finish on chairs I recommend spraying with a good enamel like Rustoleum. It is self priming, leaves a factory like finish and is very durable.

If using latex or other water based paint, I would use a spray shellac based primer like Kilz to keep the current wood stain from bleeding through your paint at a later date, and a finish coat of poly-acrylic (water based) over your paint choice. You can spray it on, brush it on and they even make some that you can wipe on. If you choose to use wax, remember it is not a permanent finish, it wears off and has to be re-done. It is just wax.

I recently painted some barstools using Valspar furniture paint (love it!) and sealed with three thin coats of Dixie Belles gatorhide and can't believe how solid but smooth it make sure the finish.