As a devoted husband promises to pursue unorthodox offer on vacation (8)
I believe the answer is:
uxorious
'as a devoted husband' is the definition.
'promises to pursue unorthodox offer on vacation' is the wordplay.
'promises' becomes 'IOUs' (promises to pay a debt).
'to pursue' says to put letters next to each other.
'unorthodox' becomes 'ux' (I can't explain this - if you can you should give a lot more credence to this answer).
'on vacation' means to remove the middle letters.
'offer' with its middle taken out is 'or'.
'ux'+'or'='uxor'
'ious' put after 'uxor' is 'UXORIOUS'.
Can you help me to learn more?
(Other definitions for uxorious that I've seen before include "Very attentive to wife" , "Fond of wife like our Sioux" , "Having great fondness for one's wife" , "Foolishly fond of ones wife" , "Too devoted to wife" .)