What legal custody means
Legal custody is the authority to make the major decisions in a child's life: where they go to school, their medical care, religious upbringing, and similar significant matters. It is separate from physical custody, which is about where the child actually lives. A parent can have substantial time with a child without holding sole authority over these decisions, and vice versa.
Legal custody can be sole, held by one parent, or joint, shared between both. Under joint legal custody, major decisions are supposed to be made together, which is why disagreements over school choice or medical care are a frequent source of conflict and, sometimes, litigation.
For documentation, the key is showing how decisions were handled. A record that you informed the other parent, invited their input, and acted reasonably speaks directly to whether joint decision-making is functioning.
Example: keeping the email where you proposed a therapist and asked the other parent to weigh in, along with their response, documents that you honored the shared-decision requirement even if you ultimately disagreed. Terminology varies by state, so confirm what your order means locally.