you also have to understand the driftmark confrontation in this context btw. she didnt genuinely love and cherish aemond as a boy and then change her mind when he grew up and one day suddenly became willing to kill him. she always saw him (and the others) as an extension of herself. the assault on his eye is an assault on her. its a slap in the face to her. her children are the physical embodiment of a sacrifice she did not willingly make and of all of her suffering and resentment because they are all borne of a child marriage she was forced into. she was imprisoned in a castle and made to squeeze out heirs at age 15 by a rotting corpse of a middle aged man while rhaenyra did whatever and whomever she wanted. she chose the fathers of all her children and the fake-fathers too. for rhaenyra's bastard love-children to maim one of alicent's unwanted children by viserys that she dutifully bore because she was told she had to, and for viserys to side with rhaenyra STILL.... is spitting on the face of this sacrifice of her body and freedom that rhaenyra has always scorned and that alicent has always resented but been powerless to escape. which isnt to say she never felt any affection for her children because i think she did and still does at some points, but the point of the scene at driftmark is not to show us that alicent loves aemond and would seek revenge for him. it is to show us alicent's resentment of the life she was forced into. her children ARE the life she was forced into. in season 2 when she fucks off into the forest alone and has a metaphorical baptismal rebirth it immediately precedes her offer of her sons lives to rhaenyra and in their confrontation tells us all of this: "i am at last myself, with no ambition greater to walk where i please and to breathe the open air. to die unremarked and unnoticed and be free."
walking outside and swimming in a lake doesnt imbue alicent with Bad Mom Son Hater Holy Water and make her suddenly switch up and be willing to kill her sons, it frees her from her attachment to them as an extension of herself and a manifestation of the injustices done to her. it is only after leaving them behind that she becomes "at last, herself" and it is as herself that she becomes willing to sacrifice them. the only "self" that remains to alicent after she has cast off this attachment to her perceived duty is someone that exists outside of (or perhaps, predates) the role of Queen Mother; she can no longer be a mother to two royal targaryen sons. helaena is an exception in alicents eyes because she is not implicated in her assigned political duty of producing male targaryen heirs. she exists outside of the "endless plotting and striving" that alicent seeks to be free of while her sons are the core of it. helaena does not trap alicent the way her sons do, of no fault of their own other than the reality of their birth, and so helaena does not so fully embody the sacrifice and suffering that festered such resentment in alicent the way aegon and aemond did. instead of being a human embodiment of her suffering, helaena and jaheara are a time machine, a second chance, they are not an extension of alicent as the manifestation of the greatest injustice done to her in her life but rather as what could have been if her mother had been there to save her from becoming what she now is.