At some points, in the various books, we see references to the scope of the story being just the galaxy. At other points there is reference to the entire universe. I've read all the books over the years and have never been able to reconcile this.
The Galactic Padishah Empire, or the Imperium, was referred to as spanning "the known universe".
The borders of colonized space are never accurately described.
During the time of the Padishah Empire, the realm seemed to be contained within the Orion Arm of the Milky Way Galaxy, and some of the core worlds (e.g. Giedi Prime and Caladan) were described as being within 20 light years of old Earth.
In God Emperor of Dune (Page 13), Leto II refers to his "multigalactic empire", so it seems that the scope has either expanded, or some components of the earlier empire were actually outside of the Milky Way.
However, after The Scattering precipitated by Leto II, the range of the "known universe" expands tremendously. At this point, it is almost certain that multiple galaxies have been colonized by humans.
It is worth noting that the Honored Matres make reference to old Imperium as the "Million Planets".
A really interesting and detailed analysis of the astronomic geography of the Dune universe can be found here.
It's true that the main narrative of the Dune novels (I've read only Frank Herbert's books, but I don't think the prequels differ) takes place in one galaxy - our own, judging by the links to Earth religions.
However, one of the main themes of the series is the Golden Path, Paul Atreides' plan to rescue humanity from its stagnation. He never got to implement it, but Leto II did, and he scattered humanity far and wide throughout the universe, far out of the galaxy. The last two novels, Heretics of Dune and Chapter House Dune, deal with those far-flung chunks of humanity returning to the main galaxy,
So yes, the story of Dune can be thought of as being in one galaxy, if you want to stick to the narrative itself, or the universe, for the whole scope.