"She does not know either."
The position of adverbs "也" (also) and "都" (all) have a fixed position. They must be placed between the subject and before the predicative verb or adjective. For example: “他们都是加拿大人” If it is a negative sentence 也 has to be before 不. And 都 can be before and after 不 but will have a different meaning. 我们都不 means "none of us" and 我们不都 means "not all of us".
I think this is just a rule. In English there are also such rules like the one for adjectives order. For example: black leather jacket. (sounds normal) But saying: leather black jacket. sounds insane.
认识 rènshi = to know things, places, people, situations personally, from personal experience, seeing, reading, meeting, having been there ... (French: connaître, Spanish: conocer, German: kennen).
我认识你。= I know you.
我认识上海。= I know Shanghai.
知道 zhīdào = to know facts (French: savoir, Spanish: saber, German: wissen)
我知道你很开心。= I know (the fact), that you are very happy.
我知道上海是一个大城市。= I know (the fact) that Shanghai is a big city.
So, as a kind of thumb rule, whenever you can add "the fact" after "know" without sounding strange, it is probably 知道.
I know (the fact) this good book. - Strange, must be 认识.
I know (the fact) that this book is good. - Sounds ok, must be 知道.