Why Did The Sea Split

In davening we say המעביר בניו בין גזרי ים סוף, we refer to Klal Yisrael as banim only when they crossed the yam suf.  Why?  

ויאמנו בה ובמשה עבדו.  The question is what happened now that caused a greater emunah, Klal Yisrael had already seen 10 maakos.  What caused an increase in emunah at this point?  Rav Itzele Blazer (Kocvay Or #3) explains that Klal Yisrael understood that Hashem controls the world and will do miracles to accomplish things for a sensible purpose.  However, at krias yam suf not only where Klal Yisrael saved, but the Egyptians were obliterated.  This was illogical to Klal Yisrael for they were cognizant of the their lowly state as the Midrash says the angels objected, both the Jews and the Egyptians were idol worshippers.  Why do the Jews deserve to be saved and the Egyptians killed?  However, when Klal Yisrael saw that they were saved and the Egyptians drowned they saw that Hashem will even do what seems opposite of logic and their אמונה that Hashem is not limited by the boundaries of human logic increased.  

(As an aside, there seem to be a contradiction in Midrashim both in regard to the makkos and krias yam suf if Klal Yisrael had a zechus or zechusim that validated their redemption or that they weren't really deserving, I'm not sure if they are supposed to be reconciled somehow and what that would be.) 

According to what Rav Itzele is explaining, Klal Yisrael did not have any clear advantage over the Egyptians to warrant the destruction of the Egyptians and yet Hashem deemed them worthy enough to destroy the Egyptians entirely.  Why?  Because they are Klal Yisrael.  They are בניו, the children of Hashem.  One doesn't need a reason to punish an attacker of one's son.  It is the natural desire, irrespective of sechel that motivates one's actions.  כביכול, Hashem stepped in to save his children.  

ויקח משה את עצמות יוסף עמו, why not say Moshe took the aron of Yosef, why the bones?  The Midrash says the yam split due to the aron of Yosef.  Why? The bones of Yosef refers to the עצם, the עצמיות, the essence of Yosef.  In the bones, the very essence of Yosef is the zechus for Klal Yisrael.  Yosef as sent to to Egypt but retained his Jewish identity in Egypt.  The merit of the aron of Yosef is that in the genes of Klal Yisrael is that עצמיות of Yosef, that connection to Hashem remained even as the externality of the Jew was not so apparent.  This is the nature of being בנים, the connection is innate (see Likutay Sichos volume 26.)