First off, great freaking job staying in set that long despite it being uncomfortable and the guy joining there. That rattles a lot of people starting out. I admire you for sticking in there. A lot of getting better with sets is just hanging in there no matter what happens until they ask you to leave. That in itself is a damn good quality to have that will get you on your way. By the way what you did is pretty much the secret to really pulling some people for dates or up to same night lays. You get in set, stay in set, build attraction, comfort, check that logistics (this part is huge) work out if they don't you can set a damn awesome date, bounce to another venue if you can, or just hang out until sex can happen.
Also good job on your cold read and friending the guy so that you don't have to deal with him as a cock block. It sounds like you guys were able to relate on some level and he realized you were a descent person and not some creep he needed to get rid of for the group.
It sounds like you had some attraction with your target for sure, but what kinds of things were you talking about with her. What did you do to relate with her like you did the guy? Attraction is important and a key ingredient for sure in getting her to like you, showing you like her, but then she needs to learn about you so she can start to know you are, and what you are about as a guy. You probably did this but just didn't post it up. Still its important to see why things didn't work.
Increasing kino can be tricky. If you have the attraction and she's comfortable with you then it should work. But you may have needed to isolate her from the group before doing it - as it may have made her uncomfortable to do that in front of her friends. Again you may have done this but didn't write it so I'm throwing it out there. Also, if you did isolate her, how long were you gone for? Did you isolate her from the group more than once?
Did you offer to try to extend the date (bounce) on the spot by taking her or the entire group somewhere? If not consider this step. It builds familiarity and really helps move things along. If you can isolate and just take her cause the group dynamics work out then great. If not don't be afraid to offer up to the whole group that you guys should go to XXXX to hang out. The more time they spend with you and in more locations the more comfortable they are with you and the easier things like setting dates and kino becomes.
I can definitely see how that got you out of your state of mind and that would really mess with me too. Keep in mind no matter what happens you just have to be cool and smile as if everything is going to plan. In my head I'd be like "oh shit!" also but you just have to keep it cool and let it pass through you like you're a ghost or something. Easier said than done I know.
Alright after they came back you got your number from your target. If you've been in set that long you should have already had her number.

If earlier in the interaction you had her number it would have been better. Then towards the end of the time with them if you had went to set a date that would have built additional rapport. She gave you her number and doesn't know if you'll call or whatever, but you set a follow up date while she's still excited from meeting you then it eliminates her worrying about you not calling and stuff. Plus it is easier to do that then while she's all OMG I'm attracted to him than later when she's cooled off a day later or so. Then all you have to do is call to confirm she can still go or pick the final time you'll meet her or pick her up.
All in all you did well. I would just encourage you that once you have attraction built where she's into you, and you show you are into her as well then you should get her number at that point. Then as things progress and you work to build more rapport with her by getting her talking about herself, and doing a bounce "instant date" then you can more easily set a Day 2 date.
It will come, you have the skills and abilities to do it. Just adjust your timing a little more. Get the # earlier in the set after attraction is firmly established. Then get her comfortable with you so she knows more about who she is going out with and she's told you about her. Then setting the date on the spot, strike while the iron is still hot.
