The Double Push for Inline is Making it's way to XC Skiing
Notice that the as the right leg pushes to the right, the left leg ALSO pushes to the left! The right leg finishes and lifts while the left foot starts turning the other direction and rolls back under the body to the left. (If it didn't, Eddy would simply fall, since both feet are to the right of his center of gravity).
Eddy Matzger says:
One key to the double push is to set your skate down underneath your body (as simple as getting your knees together), not outside it.
Another bonafide necessity is to extend your leg during the double push phase as well (see side view), since the double push is a push, and a push is not a pull and neither is the double push, otherwise it would be called the pull-push!
If you want to get actual propulsion out of the double, and not just go through the motions, extend your leg with each underpush. See how Eddy nearly straightens his leg with the double push, twice per leg before the other skate takes its turn.
Because the underpushing skate travels laterally and forward, it doesn't pop up Eddy's body all that much. A big lateral underpush causes severe instability, which could cause Eddy to topple over if he didn't whip his skate back under him to catch his weight in preparation for a huge old honking regular push.
Any pull associated with the double push is simply the unweighted, rolling recovery of your pushing skate back underneath your body, made possible by a heel carve which redirects your skate back over center line.
Enough talk. Just watch. Then do. Let us know how it goes! Thanks to Wibbit for being lazy and making me do this myself.