A brat doesn't want to win.
They want to wrestle.
They want to fight.
They want to challenge your authority.
That's why they brat.
They're not looking to overpower their Dom:
They're looking to challenge them.
They want to end up on their knees, they just don't want to go there willingly.
They want to feel that dominance and to be overcome by it. They want to poke, torment, and tease until enough is enough and they're over Daddy or Mommy's knee getting the spanking they richly deserve AND want more than anything.
A bratty sub is still a sub, they just have a different language of submission than those willing to voluntarily submit and need a Dom willing to play their game.
Remember: It's a game they want to lose, but they're going to make you earn that victory and will always test you to see if you have what it takes to win.