Tullus “Nuntiate” inquit “regi vestro regem Romanum deos facere testes uter prius populus legatos res repetentes superbe dimiserit, ut in eum omnes huius belli clades vertant!”
Haec nuntiant domum Albani.
Albani Legati nuntiant regi suo id quod Tullus dictum erat? (?)
Cur nuntiant + accusativus ?
I’m guessing it has a sense of bringing news back to their territory…
I believe the second part of this answers your question (I’m hardly an expert, so take my word with a grain of salt; I suppose I ought to have left this to those with more Latin experience than I have, but I guess part of this post is checking my own grasp of grammar):
I think swtwentyman is right that this is the adverbial use of accusative domum to mean “to home” or just “home” (motion toward). It seems odd here after nuntiant–I would have expected domi, “at home”–but that’s how the text of Livy reads, so it must be good Latin.
Many thanks.