She didn't love her son and she couldn't work out why (she was searching on the Internet for answers). She should have gone to the doctor and this might never have happened, but she didn't. She put her own fear about losing her children above her son's safety.
She beat him, and she couldn't understand why she did this to him when she didn't feel this way about her other children. She should have put him somewhere where he would have been safe from her, but she didn't. Again, was she afraid of losing her other children? Being judged to be an evil person? Sadly, she put herself first with tragic consequences.
No, from what I've read she didn't want him dead and didn't plan to murder him. She was responsible for his death and her actions lead directly to it. At any time before he died she could have taken him to the doctor and she chose not to do that.
She will live with her actions for the rest of her life. She will be separated from her surviving children, potentially for the rest of her life and I should imagine their relationship will be permanently damaged whatever, plus she will know that she has damaged their childhoods and put them through horrific trauma.
I don't think she's a danger to the public. I don't think she will hurt a child or anyone else again. I think the sentence is proportionate and the loss of her liberty and her family is a severe and just punishment.