How would you go about querying the second book in a series of novels?
Partials and even fulls were requested for the first installment, but didn't catch an agent.
I've continued the story universe, in one case with a new female protagonist, and in the other with the sole surviving 2nd main character from the first.
Both new stories can stand alone--with only minor references to theprevious ones.
Should I even mention the first book in the query?
No. It's not a second book unless there's a first. And by first, I mean a published book.
I'm perplexed why you're querying book two if book one didn't get a deal. Have you gotten assistance on the book? By assistance I mean someone other than you or your crit group taking a look. If you just keep going without fixing what was wrong, it's going to be hugely frustrating.