OP=Spot on

Agreed.
And then Vinny gives that speech with the card trick so it looks like he got some extra motivation.

I don't think you could blame him for firing Vinny up until that point all he had done was screw up.

Yes, I saw that.
I am now adding my agreement, also.

Yes that's why I said:
I agree with the OP.
Hey! You're not old enough to drink! Now go and die for your country!!!

So, the original poster is correct:
What makes you think Gambini wants you back, you obnoxious a-hole?

When Vinny is first brought into the boy's cell Bill is asleep and Stan thinks Vinny is a convict who intends to rape them.
Vinny: Excuse me, but I think a modicum of gratitude would not be outta line here!
Stan: You think I should be grateful?
Vinny: Yeah! I mean it's your ass, not mine. I think you should be grateful. I think you should be down on your beep knees.
Stan: I didn't know your visit was such an honour.
Vinny:
I'm doin' you a favour. You're gettin' me for nothin
', you little fck.
Hey! You're not old enough to drink! Now go and die for your country!!!

I don't recall that scene exactly.
Did he say "
you are getting me for free
" to both guys? Or just to his cousin (Ralph Macchio)?

he may as well get two salaries
Didn't Vinny say in the jail cell 'you're getting me for free you little beep I agree with the OP.
Hey! You're not old enough to drink! Now go and die for your country!!!

Well, if he was arguing on behalf of both anyway, he may as well get two salaries (fees) instead of just one.