can you imprisoned if you let your children 3 years old to the
movie with parents with a pg13 rating?

Greetings turnippipe!

No, a parent can not be imprisoned if their 3-year old child attends a
PG-13 rated film with them.  As pointed out at filmratings.com, "the
ratings system is strictly voluntary and carries no force of law." 
The ratings aren't on law books anywhere - they are voluntary
guidelines used by movie theaters.
"Everything You Always Wanted To Know About The Movie Rating System":
http://www.filmratings.com/questions.htm#Q6

Additionally, while the "R" rating means that people under 17 require
accompaniment by parent or adult guardian, a "PG-13" rating simply
means that some material may be inappropriate for children under 13. 
Those under 13 can still attend the movie on their own.  So if a
hypothetical film-loving 3-year old had enough cash and the means to
get to their local movie theater (perhaps via a Big Wheel?), she could
attend the current screening of "The Lord of The Rings" all by
herself.

Here is the specific definition of "PG-13" as written by the Motion
Picture Association of America (MPAA):

"Parents Strongly Cautioned. Some material may be inappropriate for
children under 13. This signifies that the film rated may be
inappropriate for pre-teens. Parents should be especially careful
about letting their younger children attend. Rough or persistent
violence is absent; sexually-oriented nudity is generally absent; some
scenes of drug use may be seen; one use of the harsher sexually
derived words may be heard."
above text from "What do the ratings symbols mean?":
http://www.filmratings.com/questions.htm#Q5

The above site also provides a database of films so that you can see
why (recent) movies were given certain ratings.  For example, if you
go to http://www.filmratings.com/ and put in Lord of the Rings into
the search box, you will be told that the film was "Rated PG-13 for
epic battle sequences and scary images."
"Reasons for movie ratings":
http://www.filmratings.com/

You can also read more about the voluntary movie ratings at the Motion
Picture Association of America (MPAA) site:
"Movie Ratings - How it Works"
http://www.mpaa.org/movieratings/about/index.htm

Jack Valenti, the president of the MPAA, also includes some additional
information on why a film may get a PG-13 rating:
"What the ratings means":
http://www.mpaa.org/movieratings/about/content5.htm#6a

And to read a little more info on how the ratings system got started,
I suggest:
"The Roots Of Ratings"
http://www.gradingthemovies.com/html/parent_alerts/bp_ratings.shtml

I hope this information is helpful.  If you would like for me to
clarify any part of my answer or further research your question,
please let me know before issuing a rating.  Thanks!


leep-ga

Greetings turnippipe!

No, a parent can not be imprisoned if their 3-year old child attends a
PG-13 rated film with them.  As pointed out at filmratings.com, "the
ratings system is strictly voluntary and carries no force of law." 
The ratings aren't on law books anywhere - they are voluntary
guidelines used by movie theaters.
"Everything You Always Wanted To Know About The Movie Rating System":
http://www.filmratings.com/questions.htm#Q6

Additionally, while the "R" rating means that people under 17 require
accompaniment by parent or adult guardian, a "PG-13" rating simply
means that some material may be inappropriate for children under 13. 
Those under 13 can still attend the movie on their own.  So if a
hypothetical film-loving 3-year old had enough cash and the means to
get to their local movie theater (perhaps via a Big Wheel?), she could
attend the current screening of "The Lord of The Rings" all by
herself.

Here is the specific definition of "PG-13" as written by the Motion
Picture Association of America (MPAA):

"Parents Strongly Cautioned. Some material may be inappropriate for
children under 13. This signifies that the film rated may be
inappropriate for pre-teens. Parents should be especially careful
about letting their younger children attend. Rough or persistent
violence is absent; sexually-oriented nudity is generally absent; some
scenes of drug use may be seen; one use of the harsher sexually
derived words may be heard."
above text from "What do the ratings symbols mean?":
http://www.filmratings.com/questions.htm#Q5

The above site also provides a database of films so that you can see
why (recent) movies were given certain ratings.  For example, if you
go to http://www.filmratings.com/ and put in Lord of the Rings into
the search box, you will be told that the film was "Rated PG-13 for
epic battle sequences and scary images."
"Reasons for movie ratings":
http://www.filmratings.com/

You can also read more about the voluntary movie ratings at the Motion
Picture Association of America (MPAA) site:
"Movie Ratings - How it Works"
http://www.mpaa.org/movieratings/about/index.htm

Jack Valenti, the president of the MPAA, also includes some additional
information on why a film may get a PG-13 rating:
"What the ratings means":
http://www.mpaa.org/movieratings/about/content5.htm#6a

And to read a little more info on how the ratings system got started,
I suggest:
"The Roots Of Ratings"
http://www.gradingthemovies.com/html/parent_alerts/bp_ratings.shtml

I hope this information is helpful.  If you would like for me to
clarify any part of my answer or further research your question,
please let me know before issuing a rating.  Thanks!


leep-ga


some search strategies used:
"pg-13" parents
MPAA ratings law

Sorry about that.  I initially mistakenly posted my Answer as a Comment.