I suggest that a party is not a good second date if you've got LTR ideas in mind. It's too early.
It's only your second date. The time you spend on your first few dates should be quality one-on-one but infrequent. You're trying to qualify this girl and increase her IL in you. With everyone else around at the party, the time you spend together is not quality because your attention will be split among many people. You'll be using up a date without raising her IL.
She will be comparing everyone at the party with you. At this early stage in her IL it would even be better for you if she was at the party by herself than with you there because if things are going well so far her impression of you will be better than reality.
I assume that the party is a Friday or Saturday, which tells her that she's your best option going, and you're already introducing her to your friends. This will probably lower her IL.
By arriving at the party together you're establishing yourselves to others as a couple, even if you're really not. Maybe you can use that to your advantage, but it would hurt me if I was trying to meet women at this place. After all, this is only a second date.
