Omitting a relative pronoun

Question

1. It is not generally acceptable but sometimes reading a book difficult to understand is good to improve intellectual thinking.

2. It is not generally acceptable but sometimes reading a book that is difficult to understand is good to improve intellectual thinking.

Which of the two sentences is correct ? (I wrote the sentences myself.)

Can I omit 'that is' in the sentence?

If not, could you please explain it clear why it does not make sense?

And I have heard about the rule that a subject-relative-pronoun cannot be reduced with the verb of its relative pronoun, could you tell me that for what reason the rule is made?

I assume that it be the reason to avoid misunderstanding meaning of a sentence, but I am not quite sure whether my assuming is correct or not.

Answer 1

Why do you need the "but sometimes"? That unnecessary bit is ruining your sentence and increasing the ungrammaticality. Note that saying "not generally accepted" already states the "sometimes" nature of the proposition.

Here is your sentence, without the "but sometimes" and cleaned up (note that I changed "acceptable" to "accepted":

It is not generally accepted that reading a book that is difficult to understand is good for improving intellectual thinking.

If you're overly concerned about removing the "that is" from it:

It is not generally accepted that reading a difficult-to-understand book is good for improving intellectual thinking.

You can cut it down even further:

It is not generally accepted that reading a difficult book is good for improving intellectual thinking.

Or even:

It is not generally accepted that reading a difficult book can improve intellectual thinking.

Answer 2

The pattern is

It is **good to do** {something} (in order) to {achieve a goal}.

It is good to do stretching exercises in order to stay limber.

And we can make a general statement without explicitly mentioning the goal:

It is good to do stretching exercises.

The predicate "it is good" is complemented by an infinitive construction:

It is good {TO DO {something} }

to do {something} is a subject that has gotten bumped out of subject position by so-called "dummy It". It has been "extraposed". Here it is not extraposed:

To do stretching exercises is good.

Your sentence follows the pattern at the top, which mentions a goal, and it would follow the pattern at the bottom, where the extraposed subject is made the actual subject, if it were not for the fact that it substitutes the gerund reading for the infinitive, to read.

But it has some extraneous material unrelated to the pattern which we can strike out for the sake of clarity and simplicity:

It is not generally acceptable but sometimes reading a book difficult to understand is good to improve intellectual thinking.

And let's replace reading with to read:

To read a book is good to improve thinking.

And now let's extrapose the subject and use dummy It:

It is good to read a book to improve thinking.

P.S. The clause difficult to understand is simply a modifier of book, a book [which is] OR [that is] difficult to understand.

Books hard to find can be expensive.