We knew you'd ask... You know who you are that we had to provide a definition :) Believe me, it was hard for us too, but put the “dressy” into casual. Dressy casual is slightly more elegant style of normal casual wear but doesn’t need to be cocktail attire.
We love your kids, we really do. But, we want our wedding to be your night off.
If you invitation says "and Guest" then yes. If not, we'd prefer if it was just you.