Then if your son is seeing that, he's seeing these corrosive attitudes. He's learning that granny is nicer to him because he's a boy.
Honestly, I wouldn't want her around my child. I wouldn't want my child quietly watching the dynamic, seeing his mother talked down to and there being an air of 'mummy is a bit crap' which he sees you accepting, tacitly.
And I'd be more worried than anything about my child 'adoring' her. Are you going to be so pleased that they had such a close adoring relationship when you see him modelling her misogynist thinking, and telling you, when he's 13, that 'I don't have to listen to you, because 'granny says you've always been useless and you're a crap mother!'
Think very hard before letting her 'inside' the dynamic of the family you have now built for yourself.
When your children are young, you are in the driving seat and can control these things, but once they're older their relationships are their own.
My parents don't see our children because I refused to let the dysfunction continue within my family. And continue it would: if people are 'inside', so are their attitudes, thoughts and feelings.
Your mother damaged you. Her relationship with your son will damage him in a different way, because she is the same person. Its about more than your realisation and taking action - it's about practicalities. 'Breaking the cycle' means just that. And it will be too late to change your mind once your son is 12 and telling you that granny says he can come and live with her and she'll look after him better so don't try and tell me what to do.