Encounter problem: husband against having pet? (3,1,4)

I believe the answer is:

hit a snag

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'pet?' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'encounter problem husband against' is the wordplay.
'encounter' becomes 'ita' (I am not sure about this - if you are sure you should believe this answer much more).
'problem' becomes 'snag' (snag can mean a problem or difficulty).
'husband' becomes 'h' (abbreviation).
'against' means one lot of letters go next to another.
'ita'+'snag'='itasnag'
'itasnag' after 'h' is 'HIT A SNAG'.

'having' is the link.

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I've seen this clue in The Telegraph.

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