"Let's go to the hospital immediately."
I think the second に must be dropped here, cause it works as an adverb with it. I cannot explain it properly, maybe someone can add some information on this.
But like the の in 一冊の本があります。 The に here connects the two words in a way, that the former describes the latter in a more distinct way.
If you were to change the scentence slightly you'd get:
Here the の drops as well.
Not a good explanation, but maybe you get my point xD
It's a different sound. びょ transcribed into English would be "byo." びよ would be "biyo."
You'll find little よ、や、and ゆ often added to the end of -い ending hirigana/katakana (such as に、み、し [and with し it would be like "sho" "sha" "shu" instead of "shio" "shia" "shiu"). Basically it just means you drop the い sound and blend it with the -よ sound.