I'm not sure what you mean by "I don't mind storing the state abbreviation in the child table, just want to avoid storing the full state name", but your main ask can be done per a typical parent child relationship.
Create the relationship making sure your two letter state code is the proxy field (this is done by default if you select the 2 letter state code as your first lookup field when creating the relationship. Otherwise, the proxy field can be set from the field properties of the Related Field on the child table).
Then, select the full state name as a second lookup field, and display it on your form.
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Mike Tamoush
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