In general, though, and especially now (because we can't forget that Shirley Temple was doing it sixty, seventy years ago, when even Hollywood had a better moral compass than it's had since), I wouldn't let my kid near the film industry for any amount of money. I mean, look at the modern success story: Drew Barrymore. Who was in rehab when she was fourteen, but she was lucky/blessed/smart enough to pull out of the downward spiral before she went full Lindsay.
Child stars have everything they could ever want, nobody reliable to teach them boundaries, and the constant squeeing adoration (and scrutiny) of millions of people. What could possibly go wrong, right? I wonder if Lindsay wishes she'd just grown up as a normal kid in suburbia and gone on to a normal career, or if that's something she can even imagine for herself. Every day of her life has been spent in a rarified atmosphere that has nothing in common with normalcy. (In this way, it reminds me of the way [non-celebrity] drug addicts live. That IS their normal.)
And yes, watching The Parent Trap (we own it) breaks my heart nowadays. Want an even sadder story? Watch *Savannah Smiles*, and then go read the Wikipedia entry about the child star in that, and then watch it again and try not to cry. Maybe it's a mom thing. She looked and talked so much like Claire did at that age.