Every school district has tutors for children who are unable to attend school because of illness. The State is not now educating the Stanley children, they have been placed in public schools in Hot Springs.
In my district, we would hire a tutor specifically for an individual child based on demonstrated critera-- the board would approve the hiring and funding for that position separately from the hiring of substitutes or regular teachers. Probably what would happen is a part time position teacher who is already hired, would have some hours added to the contract. That would be the cheapest option.
In my area, most of the substitutes would not be eligible to teach a child at home, because most are not licensed teachers. All that is required for substitutes in my area is a bachelor's degree in any subject-- a teaching license isn't required until a certain point of filling in as a long term sub.
I don't know of any districts that have a "ready reserve" of tutors on staff, sitting around, waiting for work.
Even so, all a district is required to do by law is provide access to adequate education-- not the educational method or program "desired" by the parents. Even for children with disabilities on IEPs, districts are not required to provide "the best" program available, or even the program the parents WANT. All they are required to provide is FAPE-- (free and appropriate public education), which is the source of a lot of angst between parents of special education students and school districts. The district just has to show that what they are providing is adequate or appropriate. Only when there is a complaint and hearings that whatever the school can provide is NOT adequate, will districts be forced to pay for other schools or different programs for individual students.
IMO, the Stanley kids are probably doing just fine academically and socially in public school. I'm sure the teachers and counselors know of their situation, and are looking out for them, trying to help them adjust and fit in. Most teachers are tremendously compassionate people, IMO, and these are kids in a difficult situation.