You sometimes can send a child or student to another school in another school district that the child doesn't live in however most times the student will need to reside in the location or district that they are attending public school in.
It can be difficult to get a school in another district to accept a student from another school district but sometimes you might find it possible.
The easiest way of sending a child to another school district is to move into the location where the school district is and setup residence in the new county and then enroll the student into the new school in the new school district.
Public schools are funded by tax dollars so the county would usually require that the student resides in that county to allow the student to attend the school in that district.