Each parent could be claiming one of them.
MO instructions for Nonresidents and Residents with Other State Income states: As a part-year resident, you may take either the Missouri resident credit (MO-CR) or the Missouri income percentage (MO-NRI), whichever is to your benefit. On a joint return, one spouse may take the Missouri income percentage and the other the Missouri resident credit. However, one individual cannot claim both!
The Idaho form would be based only on Idaho income so what you entered sounds correct.
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