For all the crap I've gotten for not knowing some historical dude's name, it's amazing to me what some of you "experts" are missing in terms of motivations/context clues.
Alicent doesn't just want to prevent war, she wants to prevent killing her former best friend. For three episodes now, all Alicent has done is give Rheanyra the benefit of the doubt, in conversation after conversation, to the point where it's clear that, deep down, she still cares for her. She's not some general who's thinking how *only* to save thousands of lives/prevent a war. She's a woman who's letting her feelings and her nostalgia get the best of her in that moment, which is perfectly understandable.
As for why the two of them didn't secretly meet outside the city, they literally explained this, as Rheanyra said Alicent will assume it's a trap, same as Rheanyra would if the situation were reversed.