Where was Noah's wife during the flood? Was she on board the ship with Noah or not? The fact that Prophet Noah (PBUH) prayed to G-d during the flood to save his son and only requested for his son and doesn't include his wife in that request could only mean one of two things.
Noah's wife was an infidel and traitorous woman who drowned in Noah's flood.
And it was revealed to Noah... until when our command came and the oven ran away, we said, "Take in it from each spouse two people and their family." [4.5]
The purpose of "Except for those who have already said..." She is the wife and child of Noah. 
4.Hood / Surah 11, verse 364
5. Hud/Surah 11, verse 404
6. Alusi, Shihab al-Din, Ruh al-Maani, vol. 6, p. 2543
There is no possibility of her being on the ship, as Allah specified that He saved only the believers of Nuh (AS)'s family from the flood. Allah says:
So We inspired to him, "Construct the ship under Our observation, and Our inspiration, and when Our command comes and the oven overflows, put into the ship from each [creature] two mates and your family, except those for whom the decree [of destruction] has proceeded. And do not address Me concerning those who have wronged; indeed, they are to be drowned. (23:27)
So, there are two possibilities left: she died in the flood or had died naturally or in some other way before the flood. There is no evidence in the Quran I know of to pick either one with certainty.
As for Nuh (AS)'s son being mentioned by him in dua and not his wife, that is not an evidence of anything. Nowhere do the verses claim he only made dua for his son and there was no one else he prayed for. Nor, in fact, is the possibility revoked that he knew his wife was disbelieving and thus did not ask for her, but he loved his son so much his emotions got the better of him.