Pesach sheni in the zechus of Yosef

1) Midrash Rabbah Shmos 20:17

אָמַר לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא, אַתָּה אָמַרְתָּ לְאַחֶיךָ (בראשית נ, כא): אָנֹכִי אֲכַלְכֵּל אֶתְכֶם, חַיֶּיךָ אַתָּה נִפְטָר וְיִהְיוּ עַצְמוֹתֶיךָ מְחַזְּרִין עִמָּהֶם בַּמִּדְבָּר אַרְבָּעִים שָׁנָה, שֶׁנֶּאֱמַר (במדבר ט, ו): וַיְהִי אֲנָשִׁים אֲשֶׁר הָיוּ טְמֵאִים לְנֶפֶשׁ אָדָם, וְאֵין אָדָם אֶלָּא יוֹסֵף, שֶׁנֶּאֱמַר (תהלים עח, ס): אֹהֶל שִׁכֵּן בָּאָדָם, וּכְתִיב (תהלים עח, סז): וַיִּמְאַס בְּאֹהֶל יוֹסֵף, בִּזְכוּת עַצְמוֹתֶיךָ הֵם עוֹשִׂים פֶּסַח קָטָן.

What connection is there between Yosef offering to sustain his brothers and Pesach sheni?  

The pasuk tells us that Yosef offered  וְעַתָּה֙ אַל⁠־תִּירָ֔אוּ אָנֹכִ֛י אֲכַלְכֵּ֥ל אֶתְכֶ֖ם וְאֶֽת⁠־טַפְּכֶ֑ם. Obviously he wasn't going to feed only his brothers and let their children and family starve.  Why mention וְאֶֽת⁠־טַפְּכֶ֑ם?  The Netziv points out that we find a similar pasuk earlier (47:12)  וַיְכַלְכֵּ֤ל יוֹסֵף֙ אֶת⁠־אָבִ֣יו וְאֶת⁠־אֶחָ֔יו וְאֵ֖ת כׇּל⁠־בֵּ֣ית אָבִ֑יו לֶ֖חֶם לְפִ֥י הַטָּֽף׃ and there he explains that Yosef didn't just provide a one-size-fits-all bag of groceries to his brothers to give to their families.  What you feed an adult is not appropriate for a baby.   Yosef personally managed things, אָנֹכִ֛י* אֲכַלְכֵּ֥ל אֶתְכֶ֖ם*, to make sure that each individual got what he/she needed, right down to the nitty-gritty of making sure the Gerber baby food jars were included for the babies too. 

Hashem could easily have said, "So what if a few individuals got left out of offering the korban pesach?  So long as the bulk of the people are covered, good enough."  But just like Yosef saw that each individual was cared for, so too, midah k'neged midah, Hashem took care to make sure that each individual would have n opportunity to offer the korban pesach properly.  (see the Ostrovtza for two other interpretations)

2) וַיְבָ֨רְכֵ֜ם בַּיּ֣וֹם הַהוּא֮ לֵאמוֹר֒ בְּךָ֗ יְבָרֵ֤ךְ יִשְׂרָאֵל֙ לֵאמֹ֔ר יְשִֽׂמְךָ֣ אֱלֹקים כְּאֶפְרַ֖יִם וְכִמְנַשֶּׁ֑ה וַיָּ֥שֶׂם אֶת⁠־אֶפְרַ֖יִם לִפְנֵ֥י מְנַשֶּֽׁה׃ (48:20)

R' Reuvain Katz (Dudai Reuvain) has a beautiful diyuk here  Yaakov was blessing both Ephraim and Menashe.  Shouldn't it therefore say בּכם in the plural, not בְּךָ֗ יְבָרֵ֤ךְ יִשְׂרָאֵל֙ in the singular?  

Secondly, the text of the bracha itself,  יְשִֽׂמְךָ֣ אֱלֹקים כְּאֶפְרַ֖יִם וְכִמְנַשֶּׁ֑ה, puts Ephraim in front of Menashe.  Why then does the pasuk needs to reiterate in its conclusion וַיָּ֥שֶׂם אֶת⁠־אֶפְרַ֖יִם לִפְנֵ֥י מְנַשֶּֽׁה׃?

Menashe and Ephraim each had a different role.  Menashe worked at his father's side in tending to the affairs of state.   וַיְצַ֞ו אֶת⁠־אֲשֶׁ֣ר עַל⁠־בֵּיתוֹ֮ (44:1) Targum Yonasan writes ופקיד ית מנשה דממנה אפיטרופוס על ביתיה.  Similarly, וְהֵם֙ לֹ֣א יָֽדְע֔וּ כִּ֥י שֹׁמֵ֖עַ יוֹסֵ֑ף כִּ֥י הַמֵּלִ֖יץ בֵּינֹתָֽם (42:23) Rashi writes המליץ – זה מנשה.  Ephraim, on the other hand, sat and learned by his grandfather.  Rashi 48:1: אפרים היה רגיל לפני יעקב בתלמוד, וכשחלה יעקב בארץ גשן, הלך אפרים אצל אביו למצרים, והגיד לו. Each child had his own talents, interests, skills. 

Yaakov Avinu tells us that when you bless your children, don't bless one child to be a Menashe and another child to be an Ephraim.  בְּךָ֗ יְבָרֵ֤ךְ יִשְׂרָאֵל֙, in the singular -- we should hope each and every child can excel at learning and be a talmid chacham like Ephraim, but also have the skills to make his way in the world, just like a Menashe.

That being said, make no mistake about priorities.  Yaakov put Ephraim before Menashe, and lest you think אין מוקדם ומאוחר בּתורה and what difference does it make, the pasuk reiterates וַיָּ֥שֶׂם אֶת⁠־אֶפְרַ֖יִם לִפְנֵ֥י מְנַשֶּֽׁה.