How could I write “The man painted a red house” versus “The man painted the house red”?
in Latin you can’t very well, though you can fiddle with the word order or use a cumbersome subordinate clause for the latter (“so that it was red”, “to make it red” vel sim.).
In Greek it’s easy, thanks to the definite article.
I recommend you learn Greek instead. 
Not to mention using “which was red” to disambiguate the first one too.
Vir pinxit domum, quae erat rubea. (“The man painted the house, which was red”.)
Vir pinxit domum ut rubeam faceret. (“The man painted the house to make it red.”)
Though as mwh said, it’d be more natural to say Vir pinxit domum rubeam and leave the ambiguity to context…
Resuscitating an old topic thanks to this thread, but wouldn’t an ablative solve it?
Vir pinxit domum rubro colore
seems to me to mean unambiguously The man painted the house red.