Question: It seems on Friday night that various people rise at various times towards the end of השכיבנו (and before beginning ושמרו). When is the actual proper moment to rise? (Sources, please.)

Answer: 
In the Nusach Edot HaMizrach...

> 
> הַשְׁכִּיבֵנוּ אָבִינוּ לְשָׁלום,
>  וְהַעֲמִידֵנוּ מַלְכֵּנוּ לְחַיִּים
>  טובִים וּלְשָׁלום, וּפְרושׂ עָלֵינוּ
>  סֻכַּת שְׁלומֶךָ וְתַקְּנֵנוּ
>  מַלְכֵּנוּ בְּעֵצָה טובָה
>  מִלְּפָנֶיךָ, וְהושִׁיעֵנוּ מְהֵרָה
>  לְמַעַן שְׁמֶךָ וְהָגֵן בַּעֲדֵנוּ. <>
>  וּפְרושׂ עָלֵינוּ וְעַל יְרוּשָׁלַיִם
>  עִירָךְ סֻכַּת רַחֲמִים וְשָׁלום. 
>  בָּרוּךְ אַתָּה ה' הַפּורֵשׂ סֻכַּת
>  שָׁלום עָלֵינוּ וְעַל כָּל עַמּו
>  יִשְׂרָאֵל וְעַל יְרוּשָׁלַיִם אָמֵן:
> 
> 
> 

Right where I put the <> marker is where you rise and accept the extra Neshamah of Shabbat. (You accept the extra Nefesh at the end of Lecha Dodi, and the extra Ruach at Barechu)

(Ben Ish Hai Parshat Vayera #3, Kaf HaHayyim 267:11.)

On Yom Tov it appears that one stands at the beginning of Kaddish, just as one does on weeknights. Even Sepharadim are not required to stand for Kaddish in general, the halacha is that at Arvit, one stands for Shemoneh Esreh at the kaddish immediately preceding Shemoneh Esreh.
Chabad stands before "Ufros aleinu" (See Hayom Yom, [2nd Day of Sivan](http://www.chabad.org/library/article_cdo/aid/5783/jewish/Sivan-2-46th-day-of-the-omer.htm)). It does not give a reason, but see [here](http://www.chabad.org/kabbalah/article_cdo/aid/1490225/jewish/Day-6.htm), where it quotes S'fardi prayer books as follows:

> 
> after Boi Kalah on Friday night: Think that the extra Nefesh has descended in to you. After Barchu, it tells us to think that the extra Ruach has entered, and after Ufros Aleinu, the extra Neshama.
> 
> 
> 

If that is the case, this could be the reason why we stand by Ufros Aleinu, to welcome or give respect to the extra Neshama level of the soul ([the 3rd level of the soul](http://www.askmoses.com/en/article/192,2108428/Levels-of-Soul-Consciousness.html)).

Also, some Nuschaot say "Ufros aleinu" twice in the prayer (like [here](https://judaism.stackexchange.com/questions/8499/when-to-stand-friday-night-by-haskiveinu/8503#8503) or [here](http://siddur.org/transliterations/friday-night-sabbath-services/shabbat-maariv-shema#hashk)), but the Chabad Siddur only [has it once](http://chabadlibrarybooks.com/pdfpager.aspx?req=32581&st=&pgnum=138).