The reason why anybody is entitled to go to public schools is spelled out in Plyler v. Doe, 457 US 202, that
The Fourteenth Amendment provides that "[n]o State shall. . . deprive
any person of life, liberty, or property, without due process of law;
nor deny to any person within its jurisdiction the equal protection of
Illegal immigrants, and certainly citizens, are within the jurisdiction of that state. The court explained that
The Equal Protection Clause directs that "all persons similarly
circumstanced shall be treated alike." F. S. Royster Guano Co. v.
Virginia, 253 U. S. 412, 415 (1920). But so too, "[t]he Constitution does > not require things which are different in fact or opinion to be treated in law > as though they were the same." Tigner v. Texas, 310 U. S. 141, 147 (1940).
So the question is whether the courts should defer to a state law denying illegal immigrants access to public schools. This raises the question of the kind of scrutiny / deference appropriate to such a law. The court found that public education is an intermediate case, calling for intermediate scrutiny:
Public education is not a "right" granted to individuals by the
Constitution. San Antonio Independent School Dist. v. Rodriguez,
411 U. S. 1, 35 (1973). But neither is it merely some governmental
"benefit" indistinguishable from other forms of social welfare
That is, strict scrutiny is not appropriate, but "rational basis" is too weak. Having enumerated the consequence of denying students access to schools, the court concluded that
In light of these countervailing costs, the discrimination contained
in § 21.031 can hardly be considered rational unless it furthers some
substantial goal of the State.
The goal set forth by the state was that
the classification at issue furthers an interest in the "preservation
of the state's limited resources for the education of its lawful
One apparent colorable interest is that "the State may seek to protect itself from an influx of illegal immigrants". But the court concludes that
While a State might have an interest in mitigating the potentially
harsh economic effects of sudden shifts in population, § 21.031 hardly
offers an effective method of dealing with an urgent demographic or
There is no evidence in the record suggesting that illegal entrants
impose any significant burden on the State's economy. To the contrary,
the available evidence suggests that illegal aliens underutilize
public services, while contributing their labor to the local economy
and tax money to the state fisc.
A second possibility is that "undocumented children are appropriately singled out for exclusion because of the special burdens they impose on the State's ability to provide high-quality public education". The court finds this also uncompelling, because
the record in no way supports the claim that exclusion of undocumented
children is likely to improve the overall quality of education in the
State. As the District Court in No. 80-1934 noted, the State failed to
offer any "credible supporting evidence that a proportionately small
diminution of the funds spent on each child [which might result from
devoting some state funds to the education of the excluded group] will
have a grave impact on the quality of education."
Finally it is suggested that "unlawful presence within the United States renders them less likely than other children to remain within the boundaries of the State, and to put their education to productive social or political use within the State", but again the court rebuffs this argument
Even assuming that such an interest is legitimate, it is an interest
that is most difficult to quantify. The State has no assurance that
any child, citizen or not, will employ the education provided by the
State within the confines of the State's borders. In any event, the
record is clear that many of the undocumented children disabled by
this classification will remain in this country indefinitely, and that
some will become lawful residents or citizens of the United States.
The summary is that "It is thus clear that whatever savings might be achieved by denying these children an education, they are wholly insubstantial in light of the costs involved to these children, the State, and the Nation". The law was overturned because
If the State is to deny a discrete group of innocent children the free
public education that it offers to other children residing within its
borders, that denial must be justified by a showing that it furthers
some substantial state interest. No such showing was made here.
Public school's are not, under US Constitutional law, open to all residents. However, state laws and school district policies impose relatively few restrictions on enrollment. Washington state only allows discrimination based on age group, grade level, or enrollment capacity, and specifically disallows discrimination based on location of residence. It also allows (for common schools) a school age child who is otherwise eligible and residing in an Idaho home with a Washington postal address (that is a bit odd, but it happens) to be treated as a resident of the nearest Washington district.
It is highly likely that in the case you're describing the law already admits the student for free education, but you would have to check local laws to be 100% certain. If there is a requirement that free schooling is not available to people who are not living with their parent, or whose parents are not US citizens, there is the option of suing to get that law overturned. In light of Plyler v. Doe, it seems unlikely that there would even be any such law, unless it was recently passed to get the attention of SCOTUS. That would include an interpretation of "residency" for school purposes that assert that a child is a resident of the district where his parents or legal guardian lives (i.e. a child who is for other purposes a resident would be deemed a non-resident for the purpose of school attendance).