Vague about taking sweetheart back, with wife in such a state (10)
I believe the answer is:
midwestern
'in such a state' is the definition.
(midwestern state is a type of US state)
'vague about taking sweetheart back with wife' is the wordplay.
'vague about taking sweetheart' becomes 'mide' (I can't explain this - if you can you should give a lot more credence to this answer).
'back' becomes 'stern' (I've seen this before).
'with' means one lot of letters goes inside another.
'wife' becomes 'w'.
'mide'+'stern'='midestern'
'midestern' going around 'w' is 'MIDWESTERN'.
(Another definition for midwestern that I've seen is " From South Dakota, perhaps".)