Rushed around, getting daughter to shiver (7)
I believe the answer is:
shudder
'to shiver' is the definition.
('shudder' can be a synonym of 'shiver')
'rushed around getting daughter' is the wordplay.
'around' is an anagram indicator.
'getting' indicates putting letters inside.
'daughter' becomes 'd' (genealogical abbreviation).
'rushed' with letters rearranged gives 'shuder'.
'shuder' placed around 'd' is 'SHUDDER'.
(Other definitions for shudder that I've seen before include "Shake with fear" , "Convulsion" , "Convulsive shake" , "Tremble through fear" , "Vibration" .)