A dependent child’s residency is the same as where his/her parents is/are legal residents. Each person has one district of legal residence. It is, as Old Navy said, where you live, vote, register your car, etc. If two parents who share legal ( not necessarily physical) custody of the child live in different states or districts, the candidate can choose to apply from either state/district for each SA. Not both. This determination is regardless of where the child lives or goes to school.
For example, assume one parent is military and the other not. The military parent is a legal resident of Florida. The non- military parent is a legal resident of Georgia. The family lives in Georgia. Child could apply from Florida or Georgia. This also can happen with divorced parents who live in different places. Conversely, if a kid attends boarding school in a different state/district from where the family lives, the child is not considered a resident of that (school) district because neither parent resides there.
If the OP establishes residence in a different district than where the family/ other parent lives, your child could apply from either district. However, You must meet the legal requirements to be a resident of that district. And agree with Old Navy that I’d the other “district” is near the old one, it could look bad. IOW, there ‘s a difference in perception between districts that are 300 miles away and those that are 3 miles away.
Also, just because it’s easier to get a nom from a district doesn’t necessarily mean it’s easier to get an appointment. But that’s for another day.
If you have specific questions, contact the Nominations office in Admissions.