Why is Amon mentioned here?
Rashi: I will open for them to come to Bnei Amon via Eretz Mo'av. Malbim - Bnei Kedem entered through the openings in Arei Mo'av, in order to settle in Eretz Amon.
Radak: It is because [Amon] harmed Yisrael and reviled them in their Galus more [than Mo'av], like it says "Al Bik'am Haros ha'Gil'ad Lema'an Harchiv Es Gevulam" (Amos 1:13), "Shamati Cherpas Mo'av v'Gidufei Bnei Amon" (Tzefanyah 2:8) - Amon reviled more. It says "Ya'an Amrech He'ach", "Mach'acha Yad v'Rak'acha b'Ragel va'Tismach" (3, 6). Therefore, Amon was punished more; its Onesh was repeated in the Parashah of Mo'av, for Amon and Mo'av were brothers, and their lands were next to each other.
Malbim: Amon took Yisrael's inheritance. Therefore, their punishment will be permanent. Even though it says "v'Acharei Chen Ashiv Es Shevus Bnei Amon" (Yirmeyah 49:6), we must say that it was destroyed twice. The second time, Bnei Kedem took their land, and Amon did not return. It says in Brachos (28a) that R. Gamliel forbade a Ger Amoni to Kahal Yisrael. Even though Sancheriv mixed up (exiled) all the nations by sending them into exile, "v'Acharei Chen Ashiv Es Shevus Bnei Amon" -- they already returned! The Halachah follows Yehoshua, who permitted him [for they did not return yet, just like Yisrael did not return yet, and it says similarly "v'Shavti Es Shevus Ami Yisrael."
Why does it say "u'Nsatiha l'Morashah"?
Radak: Refer to 25:4:3:1.
Malbim: This is so Amon will not be mentioned among the Goyim, since their land became in inheritance. This was Midah k'Neged Midah. It says "Ki Lo Eten Lecha me'Artzo Yerushah Ki li'Vnei Lot Nasati Es Ar Yerushah" (Devarim 2:9). Inheritance has no interruption. However, since they took Yisrael's inheritance, they were punished and their inheritance was given to Bnei Kedem. Hashem set the borders of every nation. Since Amon's inheritance was given to others, perforce they will cease to be a Goy, and they will not be mentioned among the Goyim.