OBSCURE TO MUNDANE

Pronounced differently but spelled the same,

I have many meanings, from obscure to mundane.

In a trip on a ship I get there before you,

After rain I amaze - a marvel to awe you.

One of my meanings is to acknowledge praise,

In another I move up and down as the violin plays.

I help little children, or trip they would,

I was also much favored by a notorious Hood.

Answer:

BOW

Bow (front) of a ship 
RainBOW
Take a bow
Violin bow
Shoelaces tied in a bow
Bow and arrow (Robin Hood)