The Avatar sequel might confirm his connection to Quaritch, but who Spider's mother is in Avatar: The Way of Water is a mystery. Jack Champion's Spider plays an important role in James Cameron's sequel. A human baby born on Pandora, Spider grew up on the planet and became close with the Sully family. Despite not being a Na'vi, he integrated himself into their culture as best he could. Jake Sully and Neytiri are almost positioned as his adopted parents, but the return of Quaritch in Avatar 2 comes with the confirmation that the RDA colonel is his biological father.
Spider's desire to be part of a family directly impacts his actions throughout Avatar: The Way of Water. The Avatar version of Quaritch claims that he is not the young man's father, but he eventually forms a bond with Spider. Meanwhile, the human kid becomes more uncomfortable with Neytiri's hatred of humans and the fact that she killed his biological father. The one aspect of Spider's life that Avatar 2 never touches on, though, is the identity of his mother. The answer to who is Spider's mother might not come in the movie, but the extended canon materials have provided an answer.
Spider's Mother Is Paz Socorro (Revealed In Avatar Comics)
It has been confirmed through Avatar comics that Spider's mother is Paz Socorro. While Avatar: The Way of Water takes place a decade after the first movie, James Cameron's original sequel script did not have as big of a time jump. After he determined that the script would not work for a film, he worked with Dark Horse to publish Avatar comics that adapted the screenplay. The Avatar: The High Ground graphic novels provide plenty of backstory and information relevant to the story in Avatar: The Way of Water, including the reveal of who is Spider's mother.
Paz Socorro is Spider's mom after a romantic relationship with Quaritch led to her getting pregnant. She gave birth to Spider, whose birth name is Miles (just like his father), in 2154. However, Paz Socorro died shortly after that in combat during Avatar's finale. Spider's mother was a Scorpion pilot for the RDA and flew with Quaritch's team in the attack on the Na'vi's sacred Tree of Souls. Paz Socorro was killed by the Na'vi, leaving Spider to be raised by other humans who remained on Pandora and eventually the Sully family.
Will Spider's Mom Appear In (Or Impact) The Avatar Sequels?
Since Spider's mom did not appear in Avatar: The Way of Water, it is unclear if she will do so in the future. The fact that she is dead makes it seem less likely. There is a possibility that flashbacks could be used to bring Paz Socorro into the picture. The Avatar sequels could potentially deliver a big twist and have Spider's mom return as an Avatar, following the method used to make Quaritch's return possible in Avatar 2. However, it would seem that any appearance or mention of Paz Socorro would be minor at best.
The biggest problem with having Spider's mom appear in the Avatar sequels is figuring out the right reason for it to happen. She did not have much time with Spider before her death, so flashbacks of the two of them together would not be sufficient. The workaround could come with Quaritch's development in Avatar 3 and beyond. Since the Avatar Quaritch has all the same memories as his original self, future films could show Quaritch and Paz's relationship, possibly as a way to show that he wanted a kid. This could build on Avatar: The Way of Water and see Quaritch and Spider's father-son dynamic grow.
Spider's Complex Relationship With Neytiri May Be More Important
Even though who is Spider's mom in Avatar 2 isn't known, the more important relationships by the end of the sequel for Spider are his biological father Quaritch and his adoptive mother Neytiri. Quaritch is obviously not an ideal parent for the young man, but Spider's relationship with Neytiri ends in an awkward way as she is willing to kill him in order to punish Quaritch for harming her biological parents. Surprisingly, it is Quaritch who surrenders in order to save Spider's life while Neytiri's true feelings towards Spider are shown.
The sequel's writers Rick Jaffa and Amanda Silver spoke about Neytiri's flawed actions in Avatar 2 and how they are rooted in her understandable hatred for human and what they have done to her planet. While those feelings are justified, Silver also expresses that threatening Spider's life is a way of showing the flawed aspects of Neytiri as a character, saying "Neytiri is a fully fleshed-out character. She’s got flaws. So it’s okay to let her have flaws, we think." Meanwhile, Jaffa that her decision sets up stories going forward, perhaps indicating that Neytiri's actions will cause Spider to choose Quaritch over the Na'vi.