The difference between "between" and "in between"

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May 6, 2013 16:21 meaning English phrase question
The difference between "between" and "in between"

I'm not sure about the meanings and usages of "between" and "in between."
It seems they can sometimes be replaced by each other but not always.
I'm trying to write some examples below. I wonder if they are correct, if there are any different nuances.

#1 I lay down between my two sons, who were fast asleep.
#2 I lay down in between my two sons, who were fast asleep.

#3 Insert this piece of paper between page 10 and page 11 of this book.
#4 Insert this piece of paper in between page 10 and page 11 of this book.

#5 Because of the strong wind, trains between Liverpool and Manchester are not running this morning.
#6 Because of the strong wind, trains in between Liverpool and Manchester are not running this morning.

#7 The fight between Tom and Jim lasted two hours.
#8 The fight in between Tom and Jim lasted two hours.

#9 Set the two white plates on the end of the table and the yellow one in between.
#10 Set the two white plates on the end of the table and the yellow one between them.

#11 I'll be out of town between April 29th and May 6th.
#12 I'm available until April 29th and after May 6th, but not in between.

I doubt that #6 is correct.
As for #10 and #12, I think I can't replace "between" with "in between" automatically, so I changed the sentence partly.