The chillul Hashem to give up your live is chillul Hashem is not the regular chillul Hashem -- see below.
By the 4th graders, if they might cause a real chillul Hashem (not just PR for the Jewish community) they should not go to the museum (see the end of the halacha "One who could, however, escape and flee from under the power of a wicked king and fails to do so is like a dog who returns [to lick] his vomit.")
If a child under the age of 13 makes a scene in the museum, it would not constitute a chillul Hashem, (i understand chillul Hashem means doing something against G-d's will, children are not obligated by G-d to do anything so if they misbehave it is more a chillul for the teacher since it is his will that they are not listening to)
I do not know what gives the right for a teacher to make a judgment of a child and declare that the child is responsible for a chillul Hashem.
Rambam Mishneh Torah » Sefer Madda » Yesodei haTorah - Chapter Five:
However, if he forces him [to transgress] with the intention that he
violate [a mitzvah] in the presence of ten Jews, he should sacrifice
his life and not transgress. [This applies] even if [the gentile]
intended merely that he violate only one of the [Torah's] mitzvot.
All the above [distinctions] apply [only in times] other than times of
a decree. However, in times of a decree - i.e., when a wicked king
like Nebuchadnezzar or his like will arise and issue a decree against
the Jews to nullify their faith or one of the mitzvot - one should
sacrifice one's life rather than transgress any of the other mitzvot,
whether one is compelled [to transgress] amidst ten [Jews] or one is
compelled [to transgress merely] amidst gentiles.
If anyone about whom it is said: "Transgress and do not sacrifice your
life," sacrifices his life and does not transgress, he is held
accountable for his life. When anyone about whom it is said:
"Sacrifice your life and do not transgress," sacrifices his life and
does not transgress, he sanctifies [God's] name. If he does so in the
presence of ten Jews, he sanctifies [God's] name in public, like
Daniel, Chananiah, Mishael, Azariah, and Rabbi Akiva and his
colleagues. These are those slain by [the wicked] kingdom, above whom
there is no higher level. Concerning them, [Psalms 44:23] states: "For
Your sake, we have been slain all day, we are viewed as sheep for the
slaughter," and [Psalms 50:5] states: "Gather unto Me, My pious ones,
those who have made a covenant with Me by slaughter."
When anyone about whom it is said: "Sacrifice your life and do not
transgress," transgresses instead of sacrificing his life, he
desecrates [God's] name. If he does so in the presence of ten Jews, he
desecrates [God's] name in public, nullifies [the fulfillment of] the
positive commandment of the sanctification of [God's] name, and
violates the negative commandment against the desecration of God's
Nevertheless, since he was forced to transgress, he is not [punished
by] lashing, and, needless to say, is not executed by the court even
if he was forced to slay [a person]. The [punishments of] lashes and
execution are administered only to one who transgresses voluntarily,
[when the transgression is observed by] witnesses, and [when] a
warning [was given], as [Leviticus 20:5] states concerning one who
gives his children to [the worship of] Molech: "I will turn My face
against that person."
The oral tradition teaches [that we can infer]: "that person" and not
one who is forced [to transgress, who transgresses] inadvertently, or
[who transgresses] because of an error. If, concerning the worship of
false gods, which is the most serious [of sins], a person who is
forced to worship is not liable for karet, nor, needless to say,
execution by a court, how much more so [does this principle apply]
regarding the other mitzvot of the Torah? [Similarly,] regarding
forbidden sexual relations, [Deuteronomy 22:26] states: "Do not do
anything to the maiden."
One who could, however, escape and flee from under the power of a
wicked king and fails to do so is like a dog who returns [to lick] his
vomit. He is considered as one who worships false gods willingly. He
will be prevented from reaching the world to come and will descend to
the lowest levels of Gehinnom.