Disagreement at home after exercise (5)

I believe the answer is:

runin

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'disagreement' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'home after exercise' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'after' means one lot of letters go next to another.
'exercise' becomes 'run' (running is a type of exercise).
'in' after 'run' is 'RUNIN'.

'at' is the link.

Can you help me to learn more?

(Another definition for runin that I've seen is " Argument - arrest".)

I've seen this clue in The Daily Express.

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