What is the significance of the fact that the older sister called her son 'Mo'av,' and the younger sister called her son 'Ben Ami'?
Rashi: 'Mo'av' explicitly means from her father. 'Ben Ami' is more modest. 1 She was rewarded in the days of Moshe. Yisrael were commanded not to start up with Amon at all; whereas due to the lack of modesty on the part of the older sister, they were forbidden to fight with Mo'av but they were permitted to frighten and to plunder them. 2
Targum Yonasan says that also 'Ben Ami' means the son of her father. Radak explains, "from my family."
Moshav Zekenim: Bava Kama 38a says that because the older began the Mitzvah, she merited entering the monarchy six generations earlier! The act itself was proper, but it was improper to publicize the matter.
On what merit did Lot's daughters give birth to two great nations?
Seforno: Because their intentions were pure, as the Pasuk says in Mishlei (3:6) "Know Him in all your ways" - even if sometimes it might be in the form of a sin. 1
Like we find with Ya'el, who was intimate with Sisera, in order to bring about his death, and which Chazal refer to as an Aveirah li'Shemah (Nazir 23b).
QUESTIONS ON RASHI
Rashi writes: "She received her reward in Moshe's time; Regarding Amon, the verse writes, 'Do not start up with them' at all (Devarim 2:19)." Merely because their ancestress was modest, Bnei Yisrael would not bother their descendants?
Maharal #1 (Chidushei Agados Vol. 2, p. 26; to Nazir 13b): The Amonim themselves were more modest, following the trait of their mother, and they were thus more closely associated with Bnei Yisrael.
Maharal #2 (Nesivos Olam, Nesiv ha'Tzeni'us Ch. 3, p. 109): Modesty means concealing oneself, and brings about protection; Amon was thus protected by HaSh-m's command.