For the Idaho part-year return, your mother would report 1/2 of her interest/SSA income , your father would report 1/2 of her interest/SSA income (as nonresident/Idaho source income). The Idaho entry in TurboTax is easy because you do not have to distinguish whose income it is- you will enter the amount of her interest/social security for the time she lived in Idaho.
For the Missouri return, a part-year resident can take either the Missouri resident credit or the Missouri income percentage, whichever provides the greater benefit. Because Idaho is a community property state, you can try both ways to see which is better.
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