My answer was: "They are happy birds and fathers" :( why is it wrong? because of the structure?
to be "they are happy birds and fathers" must say "kirini hontesse kepī issi"
That is not accurately specifying what is happy. I would interpret that as "They are fathers and happy birds" most of the time since it could mean either since there is no way to differentiate whether only the birds are happy and the fathers are unspecified as to their happiness or if the entire group of birds and fathers are happy. If you really meant to specify that both the fathers and the birds are all happy then it is far less ambiguous if you just say "Hontesse kepī kirini issi."
You are correct but your comment is lacking an explanation for why it has to be structured that way.
When dealing with copulas like "issi", you should follow the rule of putting the adjective directly before the noun that is modified. Otherwise use the adjective as the object of the copula.
They are happy boys and girls - Taobi riñī kirini issi
They are boys and happy girls - Taobi kirini riñī issi
They are girls and happy boys - Kirini taobi riñī issi
It's been a while since this comment, but you should know that this answer is now accepted.
Notice that it's kepī, not kepi. the long ī indicates that it's "and fathers" rather than "fathers" (I think).
For it to be, "The birds are happy fathers" it would have to say, "Hontesse kirini kepi issi" but the sentence shown says that the Birds and the Fathers are happy.