At the beginning of the novel, Anna's son Seryozha is eight years old, and Anna's relationship with him is the most important one in her life. In her "Character Analysis," we discuss Anna's slow move away from Seryozha as her relationship with Vronsky gets more intense. But how does Seryozha feel about Anna giving him up for the sake of Vronsky?
Well, at first, he's too young to understand what's going on. Seryozha appears initially, as all kids do in this novel, to be acting purely on instinct. His instinct tells him that something strange is going on between Vronsky and Anna, but Seryozha doesn't know exactly what. His confusion makes him "attentive and perplexed" (2.22.6) towards Vronsky, because he knows Vronsky is important to his mother, but he also gets "cold and shy" (2.22.6) because something about the relationship disturbs him.
Still, the bond between mother and son is tough to break, and even once Anna has left him behind to go and live with Vronsky, there's still something easy and accessible between Seryozha and Anna. When she sneaks in to see him one night when Karenin has gone out, Seryozha "understood that [Anna] was unhappy and that she loved him" (5.30.17). Although he has grown mature enough to realize that Anna feels fear and shame when she looks at him, he does not understand the social reasons why, and retains his instinctive feeling for her.
The final break comes when Seryozha's gotten a bit older. He's undergoing education (which he doesn't much like) and has grown into a handsome, active young man. At this point in his life, he has repressed all memories of his mother. He doesn't want to think about her. All he wants is to feel proud of Karenin (the only parent he has left). He's even more excited about his father's Alexander Nevsky Award (Part 5, Chapter 25) than Karenin himself is.
At this stage, Seryozha's natural relationship with his mother has finally given up the ghost, and he is slowly committing himself to life as an adult living in society. Still, no matter how hard he tries to push down any lingering feeling of loss of Anna, he still weeps for her at the end of Part 7, Chapter 19.