When is "that day"?
Malbim: It is when they will see Hashem's strength.
Why does it say "She'ar Yisrael u'Fleitas Beis Yakov"?
Malbim (Bi'ur ha'Milos): Yisrael are the great of the nation; Yakov are the lower. She'ar is what remains in its place; Peleitah is the remnant that flees to elsewhere. The former are Bnei Tziyon; the latter are those of Beis Efrayim who escaped. Even they will rely only on Hashem!
What is "Lehisha'en Al Makehu"?
Rashi: It is to rely on the kings of Egypt, who were the first to strike them.
Radak #1: Achaz relied on Melech Ashur, who (later) 'hit' him with a heavy tax that he imposed on him.
Radak #2: [He relied on Melech Ashur, who] hit him in war. Afterwards, he fought him, and now [Yisrael] realize that it is not proper to rely on man, for one must serve him and pay tax to him, and if he does not give, or [the helper] is not pleased with him, he will hit and make war with him.
Malbim: It is Ashur or another nation. Not only did [Ashur] not help [Yisrael] - they struck them! A staff can hit, or be a support. Via relying on a nation, it turned to be a staff of wounders.
Why will they rely on Hashem?
Radak: Hashem demands from man only that he rely on Him in truth 1 , and He will save him from all his afflictions. Chizkiyah did so, and Hashem struck Melech Ashur, who was striking him!
Malbim: It is even Efrayim and the 10 tribes, who served idolatry. (This is like the opinion that even a Rasha who trusts in Hashem will be surrounded with Chesed. Refer to Tehilim 32:10:3:1-5 and the notes there. - PF)
Why is Hashem called "Kedosh Yisrael"?
Radak: When Hashem struck Melech Ashur, all knew that He is Kedosh Yisrael.