Family members briefly demanding seconds behind one's back (7)
I believe the answer is:
sisters
'family members' is the definition.
(sister is a type of family member)
'seconds behind one's back' is the wordplay.
'behind' suggests the final letters.
'one's' becomes 'i's' (Roman numeral).
'back' becomes 'ters' (I can't justify this - if you can you should give a lot more credence to this answer).
The final letter of 'seconds' is 's'.
's'+'is'+'ters'='SISTERS'
'briefly demanding' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for sisters that I've seen before include "Patient attention required from such" , "Resists for relatives" , "Nuns - nurses - siblings" , "Nuns' titles" , "Resists (anag)" .)