I think you might be missing something with this question:
In the original canon--or in the "supplemented" canon, we have no reason for Vader to even know he has a surviving child. Not at first anyway.
Remember that in the original first movie, Leia and Vader cross paths within two or three scenes of the beginning. We see them portrayed as Leia Organa and Lord Vader. One, the daughter of a senator, the other, the senator's nemesis, or near enough to it. Ultimately, Leia will be revealed as Luke's sister in the "third" movie, but right now, they give no hint of any relation, even though they obviously know each other.
In that case, Vader knows her to be the daughter of Senator Organa, not his own blood. If she ultimately will be known to be likely to be strong in the Force, we see no indication of that idea yet. So..while Vader may suspect something is strange, he may not suspect enough to pursue the matter further as her likely father.
As well, when we see Vader recognize a presence he hasn't felt in some time, he seems to do so regarding Obi-Wan Kenobi, not Luke. In fact, in the first movie, Luke and Vader only barely interact; I think the only time they come close together at all is..when they're flying immediately above the Death Star. We DO see them both on the Death Star prior to the escape to the rebel camp, but most of that time, Vader pursues Obi-Wan's presence, so he may not have differentiated Luke being different...yet.
We finally see Luke and Vader duel in the second movie; that's when we learn that Vader is likely Luke's father. Even so, we hadn't learned about Anakin Skywalker and Darth Vader being the same person by then; Obi-Wan's statements don't lie about the relationship, but neither do they reveal any more than Obi-Wan can stand. ..You'll recall Luke being immensely displeased with Obi-Wan in the "third" movie when Luke and Obi-Wan meet after Yoda's death.
Even mixing the two canons together doesn't precisely present a conflict. Vader knew that Padme was pregnant with his child; he also knows she died because the Emporer told him so and because he can't feel her presence. He does not know though, that she gave birth before she died. That Padme had twins seems to be a surprise to Obi-Wan and Yoda; but by this time, they're already far away from Vader, so he can't sense the presence of two infants who're strong in the Force.
In all, this basically proves that Anakin Skywalker probably didn't think to look on Tatooine for his son because..he doesn't know that he should. He thinks Padme and any child she might've borne are already dead.