Correct! The ship in question is called the Viltgance. Explanation is as follows.

There I am, at a distance
in the calm after perilous chase
There I come, to assistance
the argenteous danger to face
We have this whole stanza worked out already. First you can see it in Lindblum, in the calm after the perilous chase through South Gate. Secondly you see it when it takes on the Silver Dragons at the portal to Memoria.

Spoken of with filial pride
when yearned for man returned
This, like I said, refers to the only time the ship is named in dialogue. Marsha, the little girl in the Lindblum Business District, tells you proudly about how her father rides a ship called Viltgance ("spoken of with filial pride"). She says this only after her father, whom she and her mother were waiting for, joins them ("when yearned for man returned").

Spoken of no more
Not mentioned again.

I hide in dual infinity turned
As we already established, "dual infinity turned" is a jerk way to say 88, which is the number of the Viltgance card in Tetra Master - its second form. Kind of a mean hint, but with a little research it could have been the key to solving it.

You're up, FFIX Choco Boy!