Could My wife needs relaxation be accepted?
Yes, thank you it's been added to the accepted translations.
Relaxation is χαλάρωση. Resting and relaxation are two different words
My wife needs to rest was marked wrong
Technically "My wife needs to rest" = Η γυναίκα μου χρειάζεται να ξεκουραστεί, with the infinitive becoming a subjunctive, i.e. verb in EN > verb in GR.
'Rest' as a noun can be translated with a noun (ξεκούραση) as shown above.
In another example "to rest" is accepted. https://forum.duolingo.com/comment/18887273
Good point, thank you for making it. :)