Sigourney's portrayal of motherhood takes it from the patriarchal passive, soft, and domestic and transforms motherhood in to a warrior ethos. For Ripley motherhood is a battle, an act of war. She is fighting the world, descending in to hell alone, to protect a little girl she barely knows, because she knows what it means to lose your entire family and be alone in the world. Ripley and Newt are symmetrical; Ripley lost her daughter, while Newt lost her family. Ripley isn't simply seeking a surrogate daughter, she's moved by compassion for a fellow survivor of the same nightmare that took her family from her.
In confronting the alien queen we see an almost unique example of a mother battling a mother. Ripley is defending her surrogate daughter while the queen is seeking revenge for the murder of her children. Each of them has hurt the other horribly, each has justification for their rage. The queen is the dark mirror of Ripley; Sending her children to die, destroying the families of others. Ripley came to LV426/Hadley's Hope to confront her nightmares and to, hopefully, help the people of the colony. Even before she knows Newt exists she has shown her humanity, her concern for others. The queen, by contrast, devoured the people of Hadley's hope. Ripley and the Queen were enemies before either knew the other existed.
In the trope of a mother defending her child, the mother is often passive; Cowering in a corner holding her children, helpless against overwhelming foes. This has been sometimes subverted in action and horror movies, and Aliens does it perhaps the best; Ripley never cowers. From the moment she hits the ground on Hadley's Hope she's a warrior. She's as terrified as anyone else, but she's a smart, competent, seasoned person; a veteran of deep space industrial transport, the only person to have encountered the aliens and survived. She is able to act in a crisis, managing her fear when others freeze or are unable to make decisions. Ripley is always acting and demonstrating agency.
The decision to rescue Newt is made by the character, not the plot. She's not simply acting out of some reductive maternal instinct. This is the culmination of her character arc - In Alien the monster invaded her home, hunted and killed her friends, destroyed her life and took her family from her. In the final act she reverses this crime; She brings fire and death to the aliens, she is the monster that hunts, she is the implacable foe they cannot stop. She takes her found family back from the nightmares. And when, in a parallel of the final act of the first movie, the alien invades the ship that will carry her to safety, she once again must fight the alien. In the first movie she was nearly helpless and uncertain, defeating the alien by guile and cunning. Now she dons a mighty suit of armor and battles the nightmare hand to hand, defeating it on its own terms in personal combat. This is her moment of triumph, battling against the dark mirror of her own heroism, compassion, and motherhood. And she triumphs, saving her friends from the nightmare, casting it in to the void of space to drift forever until the death of the last sun.
It's also worth discussing Ripley as a working class hero - A space trucker, a forklift operator. When she fights the Alien Queen she's not using military power armor or high tech weaponry. Her weapon of choice is a forklift, complete with flashing warning light and safety-yellow color scheme.
Also something to say about how Hudson and Hicks interact with the women in the story.
Hudson expresses bravado and excitement for the prospect of war, while Hicks falls asleep during the orbital insertion. Hudson is emasculated by Vasquez and his alternating between panic and bravado serves to lighten many scenes. He's overshadowed by more competent, more controlled women.
But then Hicks provides an important contrast; Hicks recognizes Ripley's competence and cedes authority to her. He's a good soldier, he knows that Ripley is a good leader and he willingly follows her in good faith. But, importantly for a movie in the 80s or today, this is not emasculating. Hicks decision to cooperate with Ripley is neither humiliating or emasculating. He remains cool, competent, and in control. The gentle flirting between Hicks and Ripley conveys mutual respect between equals. He is, without drawing attention to it, gentle and compassionate towards Newt.
So we've got Hudson who represents the stereotype of a submissive man being dominated by a "ball breaking bitch" represented by Vasquez or Ripley, but then we've got Hicks to directly subvert that - Hicks matches Ripley's competence and their mutual respect keeps Ripley from turning in to a straw-feminist caricature of a domineering woman. The movie directly addresses this stereotypical straw feminist by showing Hudson as the humiliated, submissive man, then showing Hicks as a direct subversive of that; A calm, compassionate and undeniably masculine soldier, chiselled jaw and huge gun, who has unselfconscious respect for his female peers. Hudson acknowledges that the stereotype exists, then Hicks subverts it.
It's also been commented that Hicks, Ripley, Newt, and Bishop represent a nuclear family typical of the 80s, but I think there is an important subversion; Hicks and Ripley are portrayed as equals whose relationship is built on mutual respect. Both show compassion and gentleness towards Newt, with Hicks relationship with Newt being easy and unmarked. Hicks has no problems trusting Ripley to take action or watch his back. Thus they represent a nuclear family, but it's quite different from the masculine dominated patriarchal nuclear family and represents more of a meeting of equals.