Both of them are ridiculously arrogant, in their own ways.
The only way the magic upgrade to the ancient rocket has the slightest chance of sending the kids home, is if the Praeses planned it to in advance. Yet they're all just assuming that's what it will do.
Ardent thinks his 'magic powers' will allow him to make a rocket that just happens to be able to navigate its way back to the right orbital habitat. (not just to any of the hundreds of them.) If he's wrong, they're probably both stranded on Earth or on the wrong habitat, or dead, but if he's right (and he likely is), then they're both just acting a predetermined role set out by the Praeses. In that case, he should be wondering if that's a good thing or, as Alice suggests, the precursor to a horrific war.
Gavia thinks his 'magic powers' will likely work too, and again, she really should be thinking way beyond what that means to her relationship with Ardent and her personal convenience. But she's stuck in bitter/angry mode and can't see past the end of her nose to the obvious conclusion that she's a pawn in a scary interplanetary conflict. None of this is hidden from her or beyond her understanding -- she is just too self-centered to care.
Now Alice -- she too may be missing 'what comes next'. She's totally aware of the Praeses and that Ardent and Gavia are there to manipulate Earth and probably even herself. Yet she risks her life and her town's welfare (leaving them alone for weeks) on a quest to do, it now seems, exactly what the Praeses expects her to. Shouldn't this be intensely worrying to her? Apparently she was originally motivated by a combination of kindness ("help the strangers home") and paranoia ("keep the sinister nanotech upgrades away"). Now that her paranoia is precisely what she's counting on to solve the quest, she fails to see the irony. If her paranoia is wrong, she's dooming the kids to wander in space until they run out of oxygen (so much for the kindness motivation). If it's right, she's just doing what the Praeses expects (and she's doing exactly what the enemy wants). She's just as much a pawn as Ardent here, and she's too smart for that.