This is how . . .
Set increased visits (and be specific . . . whatever number of days a week, duration, etc.) as a requirement to go on the trip with you to NYC.
If you do this, you are showing that you want to spend more time with her, but also that whether she goes on the trip (that she clearly wants to go on) is also within her control.
This is a form of blackmail for sure, but it is a positive form, and if you explain to her and make sure that you do not let contrary feelings betray you in your choice of words and tone, that you are asking for this because you "love her, miss her and want her to be more a part of your active family life," then this will do wonders.
It won't work overnight, and again, she is a teen with an onslaught of hormones, a brain that is continuing to develop, especially in the areas of cause/effect relationships. She will continue to make mistakes. You must reassure her that you love her, even when she disappoints you, and be consistent in your discipline and follow-through with consequences.
Make sure that whatever expectations you set for her are "realistic" for age and brain development. You do not want to create impossible expectations that are piled on to her. Introduce new ones slowly as her visits increase, she becomes more comfortable, etc. Try to plan fun family outings that all of you will enjoy together.
When you can, focus on the positive that she brings and make those types of comments. When children only hear complaints, disappointments, criticism and corrections from parents, they internalize that. You should have as many compliments for the complaints. Build her self-esteem rather than break it down.