Kind of family having eccentric uncle and aunt ridiculed, initially (7)
I believe the answer is:
nuclear
'kind of family' is the definition.
(nuclear family is a term for a kind of family)
'eccentric uncle and aunt ridiculed initially' is the wordplay.
'eccentric' indicates an anagram.
'and' means one lot of letters go next to another.
'initially' suggests taking the first letters.
The first letters of 'aunt ridiculed' is 'ar'.
'uncle' with letters rearranged gives 'nucle'.
'nucle'+'ar'='NUCLEAR'
'having' is the link.
(Other definitions for nuclear that I've seen before include "Relating to a core" , "Relating to part of atom" , "Concerning subatomic particles" , "Type of energy" , "Like some physics" .)