If I write a book anonymously can I write anything?

I keep trying to look it up but nothing's giving me much information. I am writing a book about my childhood and the journey me and my sister struggled with together on Wattpad. I want to dedicate a chapter on the background of my mother's childhood. Due to dramatic circumstances (she's not dead) I'm unable to speak to her and get her permission to write about her. I am keeping everyone's identity including my own anonymous. If I did speak to her I doubt she would allow me to write about her due to her abusive actions. Since everything's anonymous, is it legal for me to write anything about anyone or is that still illegal?

If I write a book anonymously can I write anything?
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