Okay, so let's first start by saying this girl is more then a friend to me, she is family. My cousin to be exact. She's had a boyfriend for a few months now and for awhile I've been nothing but happy for her, until he started cheating on her and she just says oh well and says that he is quitting la la la, even though he cheats every time she is on her period.
That's not even the biggest issue, the issue is that during the summer we were inseparable and told one another everything. We go to different schools so naturally during the school year we just migrated a little apart, still close just not together as much.
I've been pretty okay with her ditching me for this new found "love" but when I've needed her the very most to cry to over my boyfriend problems, she is too busy with her boyfriend and doesn't text or call me back. I confronted her last night about it and said that I was hurt, she texted me that I was suffocating her and she didn't have time for me between school and her boyfriend. That she didn't want to hang out because she had other engagements & she also didn't have time to text or call. She also went on to say that if we did text we should text about "silly" things and that she just wants things to be easy. So I basically responded just okay I get it and that I would give her space. I've been pretty messed up since. I've been betrayed a lot by friends in the past and now I am just completely crushed.
This wouldn't be so bad if it was the first time, but it is actually the third or fourth, I just keep forgiving her so I can have a friend, but lately (before the fight) she didn't tell me anything out of fear of me ratting her out for ditching/having sex/etc. Which in the first place I have never done that.
Anyway, bottom line is that we are family and I am trying to figure out how to move on from this devasting blow without causing a major fight within the family as a whole. I just want to see her at family functions, be cordial, and move on because this whole best friends one day enemies the next just isn't working. So is this a good idea? She texted me tonight and after 3 texts (I was being short) she quit texting me. I just am crushed and I need to know what to do that will be good for me, but not detrimental to the family.

You need to back off. Start hanging out with other people. If this girl was a true friend she would never treat you the way she has. Don't let anyone treat you like your less.