Two different things the word "custody" covers: who makes major decisions for a child, and where the child lives.
"Custody" bundles two separate questions, and conflating them causes a great deal of avoidable conflict. Legal custody is decision-making authority over major matters - schooling, non-emergency medical care, religious upbringing. Physical custody is where the child actually lives and the schedule of time with each parent. Either can be shared or held by one parent, and joint legal custody alongside an unequal residential schedule is a very common arrangement.
Courts decide these questions by reference to the child's best interests, applying factors set by state law rather than any presumption about which parent should be preferred. Many states now use terms such as parental responsibility or parenting time instead of custody, partly to separate the two ideas more clearly.
Custody arrangements can be modified as circumstances change, which distinguishes them from most civil judgments - but modification generally requires showing a substantial change since the last order, not simply a change of mind.
The jurisdiction question is the one to raise first if the parents are in different states, because filing in the wrong state can waste months. Beyond that, parents who agree still benefit from having the agreement drafted precisely enough to be enforceable - most later disputes trace back to a schedule that was clear to the parents and ambiguous to everyone else.
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