I have the latest version of the Oxford English Dictionary as an app. As much as I love you Duolingo, I believe that this holds higher authority than you hold.. regarding what is good English, and what is not. In the entry for "family" it says against the first given meaning "[treated as singular or plural]" If you accept the authority of this dictionary, then to be consistent, I think that you should keep your current answer "My family IS really happy" but also accept my answer (less prevalently used as it may be): My family ARE really happy.
I still like to try to treat collective-type nouns as plural when it doesn't sound silly. Plurals are disappearing.
I think most people would say "My family ARE really happy."
Common usage trumps both duo and any dictionary.
Like David Crystal says, "There are no common mistakes in language, if it's common, it's not a mistake."
He's a really interesting guy and well worth looking up. https://en.wikipedia.org/wiki/David_Crystal
Does anyone else think that, "My family really is happy." is a better translation than "My family is really happy." if the meaning of the sentence is something like "My family is genuinely happy."?
To me, the 2cnd one sounds like someone is using 'really' as a synonym for 'very'. Additionally, the first sentence is not even accepted as a correct answer.