OP wants appears to want child to attend public school. Student visa is possible with private school sponsorship and I-20. The link I provided earlier will permit a search for those in their area that are authorized to issue necessary documents.
OP, the road for permanent residency for the entire family is not as long as you think for a single adult child of a citizen. It is far shorter than child as a student becoming a permanent resident through employer sponsorship and then a citizen and sponsoring family.
They are fortunate you are in the position to sponsor.