Why did the Torah forbid us to allow our animals to work on Shabbos? .
Seforno: To enable the Avadin to desist from working on Shabbos.
What are the implications of the words "Shabbos la'Hashem Elokecha"?
Ramban #1: This refers briefly to remembering the Shabbos of the Creation, when Hashem rested from the work of the Creation. 1
Ramban #2: Refer to Sh'mos, 20:8:6:3*.
Ramban: And which it was necessary to mention in detail, having already done so in the first Dibros in Yisro and in other places.
Why does the Torah insert "Lema'an Yanu'ach Avd'chah va'Amoscha Kamocha"
Ramban and Seforno: The Torah inserts it here because, in conjunction with the next Pasuk ("Vezacharta ki Eved Hayisa ... "), the Torah is saying that just as Hashem removed the yoke of slavery from upon us by taking you out of Egypt, so too, should we allow our slaves to rest together with us each Shabbos. Because by doing so, when we see our slaves resting on Shabbos, it will remind us of Yetzi'as Mitzrayim. And this was not applicable by the first Dibros in Yisro, which presents Shabbos as 'Zeicher le'Ma'aseh Bereishis" and not 'li'Yetzi'as Mitzrayim'. 1
Presumably, because the Mitzvah to remember Yetzi'as Mitzrayim (which all Yisrael witnessed) is predominantly in order to 'remember' the creation, which nobody actually saw. And since the generation that had just left Egypt did not need to be reminded about Yetzi'as Mitzrayim, the first Luchos went straight to the point and presented Shabbos as a 'reminder' of Ma'aseh Bereishis.