if you let your kid alone with an adult to have sex, the potential for abuse is high.

Nonsense. This is the kind of thing that the culture has been conditioned to believe, and it is ridiculous. The potential for abuse is only high among those adults already prone to being abusive, and many of them are not deterred by laws anyway. Perhaps many are, but in a sexually open culture, children would be far more willing to discuss/report true abuse, as sex would be an open topic of conversation. The shame factor would be eliminated, and so truly abusive situations would dramatically decrease whereas healthy sexual relationships between adults and children would become the norm.

even if it was a relatively pristine affair, what if the kid wants to break up with the adult, but the adult is still in love?

As with any relationship of this sort, if one person wants to end it, it should end. Children need to be taught to speak openly of their thoughts and feelings and respected for doing so. They should have just as much say in how the relationship goes as the adult, and that should apply across the board in all relationships, even familial ones (except in cases where the child's safety is an issue.)

should the parent be chaperoning? should the adult move in with the rest of the family, maybe share a bedroom with the kid?

That would have to be worked out between all the parties involved, but as long as everyone is happy, the law should not stand in the way.

you have to draw a line somewhere, and i think that for most antis, the sooner-rather-than-later policy applies.

The line should be drawn at true (demonstrable) harm, for which there are already laws in place that should apply to everyone, regardless of age--laws against assualt, abuse, rape, stalking, etc. should do the trick just fine.