Conversation so far:
What was Rough Trade?
The Smiths then agreed to sign a record contract with Rough Trade.
Around what year was that?
CANNOTANSWER.
What record did they make?
their first album, provisionally titled The Hand That Rocks the Cradle.
How did that album do?
Rough Trade were unhappy with the album that the band produced and Troy's production of it, ordering the band to redo it with a new producer.
Why were they unhappy?
CANNOTANSWER.
Did they end up redoing it?
The follow-up singles "This Charming Man" and "What Difference Does It Make?" fared better when they reached numbers 25 and 12 respectively.

Question: Who was the new producer?
Self-contained rewrite: Who was the new producer of The Smiths album The Hand That Rocks the Cradle?