The source for these Psukim is from the Kol Bo who writes that "Some have a custom to say 'Vshamru...' before Kiddush, and after Kiddush they say different Mizmorim for the honor of Shabbos like 'Mizmor L'Dovid'."
The Pri Etz Chaim says that one should first say "Mizmor LDovid", then "Vshamru", then "Az Tisaneig al Hashem", then say out loud "Da Hi Seudasa D'Atika Kadisha" and "Borei Pri Hagafen".
The Shaar Hakolel say that the reason that the daytime Kiddush is called "Kiddusha Rabba" and not the nighttime Kiddush is because the title "Rabba" applies to anything on which the life-force of the world depends and which comes from the four letter name of Hashem.
Since at night the Kiddush says "Vayechuu hashomayim veha'aretz vechol tzva'am...Veyvarech Elokim es yom hashevyiy vayekadesh oso..." and not "Vayekadesh Hashem oso" while during the kiddush by day we say "Al Kein Beirach Hashem Es Yom Hashabbos Vayekadsheihu", the morning Kiddush is called "Rabba".
The night-time Kiddush is the sanctification of Shabbos by the Jews (therefore it is often done during Tosfos Shabbos, which was not sanctified by Hashem during creation but rather by Jews).
Therefore, in the norning Kiddush we say "Veshamru...", "Zachor..." which discusses the sanctification of Shabbos through the Jews (what was accomplished the night before), and then we say "Al Kein Beirach Hashem Es Yom Hashabbos Vayekadsheyu" which is the sanctity of the Shabbos that comes from Hashem (the Kiddusha Rabba).