(א) דין מי ששהה לבוא לב"ה עד ישתבח ובו ס"א:
אם בא לב"ה ומצא צבור בסוף פסוקי דזמרה אומר ברוך שאמר עד מהולל בתשבחות ואח"כ תהלה לדוד עד מעתה ועד עולם הללויה ואח"כ הללו את ה' מן השמים עד לבני ישראל עם קרובו הללויה ואחר כך הללו אל בקדשו עד כל הנשמה תהלל יה: הגה ואם יש לו שהות יותר יאמר הודו לה' קראו עד והוא רחום וידלג עד והוא רחום שקודם אשרי כי בנתיים אינן רק פסוקים מלוקטים [הגהות מיימוני פ"ז מהלכות תפלה]
ואח"כ ישתבח ואח"כ יוצר וק"ש וברכותיה ויתפלל עם הצבור ואם אין שהות כ"כ ידלג גם מזמור הללו את ה' מן השמים: הגה אם עוד אין שהות לא יאמר רק ברוך שאמר ותהלה לדוד וישתבח [הרא"ש והר"י פ' אין עומדין] ואם כבר התחילו הצבור יוצר ואין שהות לומר פסוקי דזמר' אפי' בדלוג יקרא ק"ש וברכותיה עם הצבור ויתפלל עמהם ואח"כ יקרא כל פסוקי דזמר' בלא ברכ' שלפניה' ולא של אחריהם: הגה ומ"מ יאמר כל הברכות שמחוייב לברך בבוקר [כל בו וב"י בשם מהרי"א] כמו שנתבאר סי' מ"ו ומ"ז:
(1) If one comes to synagogue and finds the congregation at the end of P'sukei D'zimra, he should say "Barukh She'amar" until "M'hulal B'tishbahot" (i.e. the end of the blessing), and afterwards "T'hillah L'david" until "Me-atah v'ad olam halleluyah" (i.e. all of Ashrei). And afterwards "Hal'lu et Hashem min hashamayim" until "Livnei Yisrael am k'rovo hallelulyah" (i.e. Psalm 148). And aftewards "Hallelu el b'kodsho" until "Kol han'shamah t'hallel yah" (Psalm 150). Rem"a: And if he has more time, he should say "Hodu l'Hashem kiru" (I Chronicles 16:18-36) until "v'hu rahum" (during the anthology of verses from Psalms) and skip to the "v'hu rahum" [immediately] prior to Ashrei because in between [those separate instances of "v'hu rahum"] are simply gathered verses [Hagahot Maimoni, Chapter 7 from Hilkhot T'fillah].
And afterwards Yishtabach, and afterwards [the blessing of] Yotzer [Ohr], and the Sh'ma and its blessings, and then pray with the congregation. And if he doesn't have much time, he should also skip "Hal'lu et Hashem min Hashamayim". Rem"a: If there is still not enough time, he should only recite Barukh She'amar, T'hillah L'david (i.e. Ashrei), and Yishtabah [The Rosh and the Ri from the Chapter "Ein Omdin"]. And if the congregation has already started with Yotzer and one does not have time to recite P'sukei D'zimra even with skipping, he should recite the Sh'ma and its blessings with the congregation and pray with them (ie. the Amidah), and afterwards recite all of P'sukei D'zimra without a blessing before or afterwards. Rem"a: And in any case, he should say all of the blessings required of him to bless in the morning [Kol Bo and Beit Yosef from the Mahari] as it is explained in Siman 46 and 47).
We see that from Hodu until Vehu Rachum is its own "portion" in regards to which portions of Pesukei D'Zimra one should say when time doesn't allow the entire pesukei d'zimra to be said in its entirety.
However, in regards to a halacha about hefsek, the boundary of where Hodu's portion ends is different.
(ד) צריך ליזהר מלהפסיק בדבור משיתחיל ברוך שאמר עד סוף י"ח: ואפילו לצורך מצוה אין לדבר בין ברוך שאמר לישתבח [ב"י בשם כל בו] [וע"ל סי' נ"ג ונ"ד]:
(ה) בין המזמורים האלו שואל מפני הכבוד ומשיב שלום לכל אדם.
ובאמצע המזמור שואל מפני הירא' ומשיב מפני הכבוד:
(4) One must be cautious to refrain from talking from the moment he begins Baruch She'amar until after he concludes the Eighteen Benedictions (The Amidah). Rem"a: And even if it is for the sake of performing a mitzvah one may not talk between Baruch Sheamar and Yishtabach [Beit Yosef quoting the Kol Bo][see below 53 and 54].
(5) In between these psalms one may ask [of another's welfare] out of respect [for that person] and may reply greetings to any person.
And in the middle of [one of] the psalms he may ask [of another's welfare] out of fear and he may reply out of respect.
(ד) [ד] ובאמצע המזמור וכו'. וכן בין הפסוקים הסמוכים זה לזה אפילו אינם מזמור שלם דינם כבאמצע הפרק דהיינו מהודו לה' קראו עד אמן, והלל לה'...
In the middle of a psalm etc. This also applies to portions of pesukim which we say in Pesukei D'Zimra which are close together, even if they don't make up a full psalm, they also carry the halachos of "middle of the psalm". For example, from Hodu until "Amen, V'Hallel Hashem"
My question is, why is the portion of Hodu reckoned until V'Hu Rachum in regards to Hilchos Dilug, but until "Amen V'Hallel Hashem" in Hilchos Hefsek emtzah passuk?
I'd like to suggest a possible answer which requires one to take a look at the overall content and explanation of Hodu.
From the passuk "Shiru Hashem Kol Haaretz", the pesukim begin discussing the future Time to Come when Hashem will reveal His Kingdom, all of the nations will recognize His glory, and the ensuring happiness that will fill the world.
The passuk "V'Imru Hoshieunu" until "V'Hallel L'Hashem" is a continuation of this theme:
וְאִמְרוּ הוֹשִׁיעֵֽנוּ אֱלֹהֵי יִשְׁעֵֽנוּ וְקַבְּ֒צֵֽנוּ וְהַצִּילֵֽנוּ מִן־הַגּוֹיִם לְהוֹדוֹת לְשֵׁם קָדְשֶֽׁךָ לְהִשְׁתַּבֵּֽחַ בִּתְהִלָּתֶֽךָ: בָּרוּךְ יְהֹוָה אֱלֹהֵי יִשְׂרָאֵל מִן־הָעוֹלָם וְעַד הָעֹלָם וַיֹּאמְ֒רוּ כָל־הָעָם אָמֵן וְהַלֵּל לַיהוָֹה:
And say, “Deliver us, God of our deliverance; gather us and save us from the nations, to give thanks to Your holy Name, to be extolled in Your praise.” Blessed is Adonoy, the God of Israel for all eternity, and you [plural] shall say “Amein” and give praise to Hashem.”
Who is commanding Klal Yisrael to say these things, and why?
Some meforshim say that this is an exhortation that Dovid HaMelech made to Klal Yisrael in his generation. He told them, "Although you personally may not experience galus and the absence of the Beis HaMikdash, you should pray to Hashem on behalf of your descendants in later generations who will go into galus, that Hashem should rebuild the Beis HaMikdash and reveal His glory to them.
He ends his exhortation by having them say "Amen" and another praise to Hashem.
We see from here that this portion of Hodu is somewhat self contained as the portion of "Dovid HaMelech's exhortation to Klal Yisrael to pray on behalf of later generations." Therefore, in respect to hilchos "hefsek", one should wait until he has finished a full inyan.
However, the next pesukim, althouh aren't directly connected to this exhortation of Dovid, is the closing statement of the portion of Hodu which discusses the Time to Come, and specifically the rebuilding of the Beis HaMikdash, as the meforshim say.
Therefore, in regards to hilchos dilug where the idea is to recite the main parts of davening, the halacha is to say the entire portion which discusses this topic, and the topic does indeed end after Romemu, and therefore we say until Romemu (aka V'Hu Rachum lo ad bichlal).