Soothed with sausage cooked by daughter (8)
I believe the answer is:
assuaged
'soothed' is the definition.
(I've seen this in another clue)
'sausage cooked by daughter' is the wordplay.
'cooked' is an anagram indicator (letters cooked into a new form).
'by' means one lot of letters go next to another.
'daughter' becomes 'd' (genealogical abbreviation).
'sausage' is an anagram of 'assuage'.
'assuage'+'d'='ASSUAGED'
'with' is the link.
(Other definitions for assuaged that I've seen before include "Soothed" , "mollified" , "Allayed, alleviated" , "Mitigated or relieved" , "Alleviated, pacified" .)