These things are plot necessities, but they aren't plot oversights.
Why doesn't Starfleet ask the Ba'ku pretty please, can we have eternal youth? Because the Son'a tell them the Ba'ku cannot be communicated with - they are primitives whose society would crash and burn if Starfleet as much as said "We come in peace". (Which shouldn't fool Starfleet for a split second, because a single native village of half a thousand people could never have attained the iron age technology witnessed. But perhaps the Son'a had ways to make Starfleet believe that these were the last survivors of a more widespread, truly native culture. The Ba'ku probably aren't your typical n'th generation survivors of a starship crash, either, so Starfleet would give the native theory the benefit of doubt.)
Why don't the Ba'ku ask Starfleet pretty please, can you go away if we give you eternal youth? There's no grounds for dialogue when the spying plot is first revealed; too much distrust around. There's no trust in Picard even after he turns out to be a fairly decent guy, because the Ba'ku have nothing to gain from revealing they remain forever young - it's a secret they desperately want to keep, and they don't know the aliens are already
after the very thing. (Okay, they did hold a few Son'a prisoner for a while, so they do know who their real enemies are. But that's not something they would wish to discuss with outsiders who are in obvious cahoots with the Son'a.)
And then the holoship abduction scheme is revealed, and Picard beams up right away to strangle Dougherty - so there's no time
to talk peace with either of the Starfleet stiffs. And then the guns start to do the talking.
The writers went to a lot of trouble to make it plausible
that the truth cannot be revealed. It all becomes necessary not just because the drama calls for it, but because the events
As for evacuating the kids, that would make no sense. Why not evacuate the entire population? They aren't going to score any actual points by staying. But Picard wants them to make a symbolic
stand, and those are far more effective with cute kids than without.