I don't understand why she needs Shinji, couln't she just complete third impact herself?

Yui doesn't want Third Impact at all; all her schemes are based around rejecting and reversing it should it be inevitably invoked by one of the other factions.

And yea, it's not so much whether she needs Shinji so much as he's her son, and she wants him to be A) safe, and B) happy.

To perhaps clarify everybody's intended outcomes a bit (or my opinion on them, anyway), Yui's desire is to use Unit-01 as an Ark to save mankind from the destruction of the flood of destruction that it is Third Impact and the initiation of the Human Instrumentality Project.

Nerv/Gendo's isn't entirely clear (it's made a bit hard to know exactly because of the differences between the original TV anime and Sadamoto's manga), but his ultimate goal is simply to be reunited with Yui once again. The specific ways he tries to go about accomplishing this seem to be to either becoming a single, consummate being with the whole of humanity and thus her as well, or to some how go about merging with Lilith while fused with Adam's embryo and to accomplish their forbidden union and become a part of that resulting God himself in a similar fashion that Yui accomplishes what ultimately results in that same level of being by having her soul embodied in Unit-01/Lilith's off-spring/clone, Shinji's soul in the core, and the Lance of Longinus fusing with the core and the Eva and forming the Tree of Life (to paraphrase Fyutsuki, "thus becoming God"). After becoming a Gendo GNR he would incorporate either Unit-01 or the Tree of Life (although I'm not sure how he'd know the Lance of Longinus would return the way it did in EOE, so it's debatable he would be capable of foreseeing that at all, but the end result of reuniting with Yui and to never part again would be the same).

SEELE's goal is also a bit unclear because differences in the manga and anime. They essentially either desire humanity's destruction and extinction, for all of humanity to be united as a massive single being, or, as implied in the manga, to use either Unit-01 or the Evas as their own personal Arks to avoid the rest of humanity's fate of destruction and to become false immortal gods.

So, knowing all of that, Yui's will and ultimate desire is the only one not contingent or even interested in or wanting Third Impact's occurrence. She was merely dealing with the hand she was dealt and formulated a way to ensure her goal given the eventual inevitably of Third Impact. Gendo's goal came about as a direct result of the strategy she employed to make things work. His goal also necessitated Third Impact's occurrence, either through the completion of HIP or the result of Adam and Lilith's forbidden fusion.