Alright. First things first. You're not going to get anywhere in any relationship that isn't founded on trust by the sound of it. Some people are fine with lying and all, but that doesn't work out well in the long run. From a general character analysis from what you've shown, you want honesty.
There's a very popular saying around here. Cheating is not measured in actions. It's measured in secrets. Girls can be very finicky. It's possible that this girl loves strip clubs too, would have no problem with you going except that she'd have loved to go with you.
It's equally (or more likely) possible that she will view this in a very negative light. I would recommend talking about it with her. You seem to have pretty good communication: That's the #1 thing in relationships (trust factors into this). If she has a problem, explain why you want to go. Hash it out. Decide to go or not, but include her in the discussion.
As to the beginning, you just need to get your feet wet with relationships. It all becomes much easier once you're actually involved in them. I'm glad you worked up the courage to ask that other girl out too.
GL
