Nadya had a really interesting relationship with her children. Before killing herself, she told a nurse that nothing made her happy, not even the children.
She was pretty cold around them, but she cared for them. She always wanted them to be busy. I think Svetlana once wrote about Nadya giving decent advice, even though she definitely was quite strict.
Svetlana also wrote about how once her mother "slapped her across the hands" and it made her cry so hard that Stalin picked her up and reassured her.
Here is a letter from Nadya to Svetlana: "Hello Svetlanochka:
I had a letter from Vasya saying that my little girl is carrying on and being terribly naughty. I hate getting letters like that about my little girl. I thought it was a big, sensible girl I was leaving behind, and now it turns out she's only a little girl after all and doesn't know how to behave like a grown-up. Svetlanochka, please talk to Natalia Konstantinovna and fix everything so I don't get any more letters like that. After you've talked to her, get Vasya or Natalia Konstantinovna to help you write me what you've decided. When Mama went away, her little girl made a great many promises but now it turns out she isn't keeping them.
Please write and let me know whether you've decided to be good or not.
You decide. You're a big girl and are able to think for yourself. Are you reading anything in Russian? I'm waiting to hear from you.
She loved her stepson, Yakov, and they were actually fairly close in age. I think they bonded because they both had intense mental health struggles. She was horrified when Yakov intended to kill himself.
Not much is written about her and Vasily, but according to Svetlana, she "adored" him.
She seemed to be stricter with Svetlana. But I guess we just don't know much about Vasily and Stalin. She also adored Svetlana, from what people have said, even if she had some issues, but their relationship seems more complicated and in depth. Svetlana and Vasily were also significantly younger than Yakov. I believe she and Yakov were only six years apart.
You can read a bit about them here, these are some of the main sources I use for this information:
The Tragic 1962 Death Of Joseph Stalin's Son, Vasily Stalin
How My Mother Killed Herself; By Svetlana Alliluyeva: How My Mother Died
What was Stalin’s wife Nadezhda Alliluyeva like?