Two men get extremely touchy with the King's family (7)
I believe the answer is:
royalty
'king's family' is the definition.
'royalty' can be an answer for 'family' (royalty is a kind of family). I am not sure about the 'king's' bit.
'two men get extremely touchy' is the wordplay.
'two men' becomes 'royal' (I can't justify this - if you can you should believe this answer much more).
'get' is a charade indicator (letters next to each other).
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'touchy' with its middle removed is 'ty'.
'royal'+'ty'='ROYALTY'
'with the' is the link.
Can you help me to learn more?
(Other definitions for royalty that I've seen before include "Regal folk" , "(Rank of) kings and queens" , "payment for literary work?" , "Sovereign rule" , "King or queen's status" .)