The mother later told her daughter to not attend school to avoid detection of her pregnancy, and informed the school that the girl was unwell, requesting that her daughter be withdrawn from secondary school.
Can “not to attend school” replace “to not attend school”?
Thanks.
Yes, it can. But does it matter Koohyoongliat? The message as you’ve written it, is very clear to me.
It can, and it is, traditionally.
But the question is whether we can split the infinitive or not.
In modern English, splitting is accepted, so, we say ‘to immediately complete’, ‘to not attend’, etc.
Lawrence, don’t you think it a bit strange? In my opinion Koohyoongliat asks questions to which he already knows the answer. If I know the answer to a question, I don’t ask, because I don’t like to bother other people by questions I already know the answers to. I’m not saying that the dear Chinese man has to leave the forum, but since you’re the elder, I think you should tell him where people draw the line.
I think he wants to confirm the position.
I agree. Such topics are also useful for other users as well.
As for the use of “not to + verb” and “to not + verb”, I have always taught the first instance as the correct form but I see the use of the second one almostas frequent as the second one; yet, I still cannot force myself not to use the negation before the infinitive. 
To be, or to not be, that is the question
Sorry, I had to. 
If Hamlet had said it that way, I think the line would not be nearly as famous. It just doesn’t flow as well. The tongue stumbles over it.
I think flow, aesthetics, subtleties, and ease of understanding are just as important, or more important, than established grammatical structures.
For the original question, the short answer is, “It doesn’t matter.”
Unlike the line from Hamlet, there is little difference in flow or aesthetics. Nor is there any difference in meaning except a very slight change in emphasis.
Sometimes, you absolutely want to split the infinitive, but in this case it doesn’t matter. It’s just a matter of habit.
Whether ’ is nobler in the mind to suffer the slings and arrows of outrageous fortune,
or to take arms against a sea of trouble… Yes, I know, NN. You see, Hamlet became desparate at a certain moment, but the strange thing is that some historians use this text to indicate that Elizabeth I had become very depressed, if I may call it that way. You see, all of her friends, including Baron Burghley, also known as William Cecil, her Secretary of State and others had passed away. Although, I do not write about kings and queens all that much, the Tudors Era has always interested me. You see, I first got into contact with them, so to speak, when my mother told me on a Saturday afternoon, there’s a film on television with Flora Robson. Later on, I decided to write a dissertation on the Tudor Era and after I had handed it in for the pro’s to read it, I just couldn’t stop looking for information about that glorious era in history. Then I saw the series Elizabeth R starring Glenda Jackson and after that the films ‘Elizabeth’ starring Cate Blanchett came out. Coincidence or not?
First, a warning. I was well into middle age before I knew what was meant by splitting an infinitive.
“To not attend”
“Not to attend”
Here I think the important thought is not attending school. I looked up some antonyms for attend and didn’t get anything good. Ditch and foresake would fit grammatically but don’t carry the same thought. I think putting not adjacent to attend gives the main point of the sentence more emphasis, as if we were using an antonym, and is almost like saying that the verb is not attend.
Do you mean like using it as a gerund. Her mother told her to not attending school…? It doesn’t sound wrong or unnatural at all and it does make sense, at least to me it does.
You could use a gerund in your sentence and I’ll rewrite it with one: The mother later told her daughter not attending school would be better to avoid…
I looked it up, it is possible and understandable, however, the first version I gave you, well, I recommend it. It’s easier for readability.
Yes, we have been used to writing or listening to: To be, or not to be; not otherwise!