You would report 100% of the 1099-DIV on your return and then you'd add a line that you describe as "Nomineed to [censored]-xx-xxxx" and then put a negative 1/3 of the total in that box. I'd give ex a copy of the whole 1099 to ex and they'd report their 1/3 on a line titled "Nomineed from [censored]-xx-xxxx". You dont file a 1099, you receive one and report it.
For the stock sale, you would do the same thing, report the whole sale (on both, the reason is so that the 1099's match what is filed, the nominee portion is irrelevant to the actual 1099, not reporting the whole 1099 could hold up your filing when what you report doesn't agree to what is reported by the 1099 filer) and then 'nominee...' her portion and she will show the sale on hers as 'nomineed from...'
Eternity is too long to be wrong.