Does a minor saying, "I want my mommy" have the same legal effect as an adult saying, "I want my lawyer"?
If a suspect in police custody asks for a lawyer, the interview must stop.
If the suspect invokes [assistance of counsel during custodial interrogation] at any time, the police must
immediately cease questioning him until an attorney is present.
Davis v. United States, 512 U.S. 452, 114 S.Ct. 2350, 129 L.Ed.2d 362 (1994)
This is known as the Edwards Rule because it was born in Edwards v. Arizona, 451 U.S. 477, 101 S.Ct. 1880, 68 L.Ed.2d 378 (1981)
It doesn't work this way in school because interrogations by school officials are not subject to Miranda. This is important because the reason for the Edwards Rule is preventing officers from badgering a suspect into waiving his previously asserted Miranda rights. See Davis.
There is no authority requiring a school administrator not acting on
behalf of law enforcement officials to furnish Miranda warnings.
Com. v. Snyder, 597 N.E.2d 1363, 413 Mass. 521 (Mass., 1992)
New Jersey v. T.L.O., 469 U.S. 325, 105 S.Ct. 733, 83 L.Ed.2d 720 (1984) held that teachers and school administrators do not act in loco parentis in their dealings with students. "In carrying out searches and other disciplinary functions pursuant to such policies, school officials act as representatives of the State, not merely as surrogates for the parents."
The point to all that is to say that school officials do not need to change course at all when a student asks for a parent.
Schools do need to question students.
A school official must have leeway to question students regarding
activities that constitute either a violation of the law or a
violation of school rules. This latitude is necessary to maintain
discipline, to determine whether a student should be excluded from the
school, and to decide whether further protection is needed for the
student being questioned or for others.
State v. Biancamano, 666 A.2d 199, 284 N.J.Super. 654 (N.J. Super. A.D., 1995)
Perhaps the better way to ask the question is - if the school interrogates the child and refuses to contact a parent upon request by the child, is there any recourse by the child or his family?
20 U.S.C. § 6736(a)(2) provides immunity for teachers:
(a) Liability protection for teachers Except as provided in subsection
(b) of this section, no teacher in a school shall be liable for harm
caused by an act or omission of the teacher on behalf of the school
if...the actions of the teacher were carried out in conformity with
Federal, State, and local laws (including rules and regulations) in
furtherance of efforts to control, discipline, expel, or suspend a
student or maintain order or control in the classroom or school.
States have passed their own similar laws. For example, Colorado:
(1) An educational entity and its employees are
immune from suit for taking an action regarding the supervision,
grading, suspension, expulsion, or discipline of a student while the
student is on the property of the educational entity or under the
supervision of the educational entity or its employees
So, if a student is being questioned by a teacher or administrator, and asks for a parent, there is no federal or state law which requires the interview to stop.
Once arrested, the parent question varies by state and you get some information about this in the link you provide. This memo does a good job of summarizing a few states' laws. Basically, most states require the police to initiate various levels of parent involvement for kids under 18. Some states make exceptions to this rule for 16 and/or 17 years olds.
Also, many state laws require certain action by the school (in regards to contacting parents) when police come to the school to interview students. There is an amazing volume called Compendium Of School Discipline Laws And Regulations For The 50 States, District Of Columbia And The U.S. Territories which provides a lot of these rules.