In a formal contracting situation, we would want to see Dakota Fanning receive something like an allowance in return for agreeing not to get a tattoo. Of course, that’s not specified, and the presumption given the small amount of information we have is that Ms. Fanning’s consideration was not being harmed by her mother (not in a physical way, just in a way that would make Dakota’s young life less pleasant). And although that sounds coercive (and likely is), it is at least possible that it could still be construed as consideration.

I am sure that it has been argued before that withholding unpleasantness constitutes a benefit to another party, and can therefore be consideration for an agreement. Personally, though, on the face of it that seems much more like coercion than consideration to me.

So it’s likely that it’s not a contract on the grounds of lack of consideration as well.