I think that is the breather tube for the front axle, but you may want to wait for others to confirm that.
I don't think that that being disconnected would have anything to do with you sputtering. I don't know what the flashing check engine light is all about, but have you ever changed your fuel filter or fuel pressure regulator? If either of those is bad that could cause the sputtering. Also, have you changed your PCV valve (it tends to get clogged), or cleaned your EGR? All of these could contribute to sputtering, but you'll probably have to have the engine code read to find out why the CEL is flashing.
"The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong, it usually turns out to be impossible to get at or repair."
-Douglas Adams, Mostly Harmless