The meaning of the sentence is correctly conveyed in the first sentence

the book illustrations are coordinated with narratives

which correctly refers to illustrations.

In the second sentence the use of 2 back to back modifying phrases in incorrect on the GMAT.

can you explain further? What is back to back modifying phrase? why is it not accepted in Gmat?

Anliv wrote:Beatrix Potter, in her book illustrations, carefully
coordinating them with her narratives,capitalized on
her keen observation and love of the natural world

Which will be right answer?
In her book illustrations, which she carefully coordinated with her narratives, Beatrix Potter
or
In her book illustrations,carefully coordinating with her narratives, Beatrix Potter

The answer from OG is the 1st choice, nut I don't know why?
And when do we use "which-clause", when do we use gerund??

1) Whenever a phrase comes between a comma, it modifies the preceding noun by bringing additional info. Also, be little cautious when two 2(or more) such phrases come together.
The original sentence can be read : Beatrix Potter,ignore,carefully coordinating them with her narratives,capitalized on her keen observation and love of the natural world.

Actual meaning the author wish to convey is: Beatrix Potter capitalized on her keen observation and love of the natural world.

Now we wish to modify "Beatrix Potter".
Correct 1: In her book illustrations, Beatrix Potter capitalized on her keen observation and love of the natural world.

Now we wish to further modify\add info "Illustrations"
Answer \ Correct 2: In her book illustrations, which she carefully coordinated with her narratives, Beatrix Potter capitalized on her keen observation and love of the natural world.


Also, note how both the above correct sentences, keep the actual sentence together and complete modifier at the beginning[in this case] of the sentence

Coming to
Option: In her book illustrations,carefully coordinating with her narratives, Beatrix Potter

In this option it seems ILLUSTRATIONS are COORDINATING. This is incorrect. Actually its Beatrix who coordinates. Moreover the correct option says "illustrations, which she carefully coordinated", thus clearly mentioning who coordinated.

I hope this helps !!