17/m in a relationship with issues

Hey! I just wanted to send you a quick thanks for the tour. Your labs and the campuses are awesome. Definitely applying next year.

Jake KincerAlright, so this will be pretty long winded, please refer to the TL;DR if you get bored.*
I guess I should start by saying that I have pretty large jealousy and trust issues. My gf has lied to me about her past and a few other things a multitude of times, and I've given her multiple q's chances" to be truthful. This is the-to my current knowledge- full story from where it becomes relevant. I'll explain the issue once I've dispensed the information. My current GF and I started talking this time last year, after she had been in a very on again off again relation ship with this guy, we will call him J, but when I went on summer vacation to Europe, she got back together with this guy and they had sex, for the umpteenth time(the amount and other details has varied wildly, at first she said every day for 8months and. Ow it's down to a few times a week for a few months. Keep in mind she changed what she said many times). He promptly broke up with him and sent me a message saying she would never go back toy I'm again etc. so I'm like okay and attempt to start a relationship with her when I get back, but she blows me off. Instead she begins dating tis next guy, lets call him D, and they fool around but nothing else (although at first she told me the had sex). Then she went to a family reunion and got extremely drunk and blew and otherwise fooled around with one of her cousin (she completely denied it at first and got mad that I questioned her even though one of her friends had hinted at it, this includes lying to my face several times. Its also important to note that this cousin is distant and non blood related). Then she broke up with D for reasons unknown and immediately started flirting and talking to me amongst a few other guys and went to football games or movies (minor dates) wih almost all of us without any of us knowing. Then in October one of her friends sexually assaulted her (tried to rape her but didn't get in, she and he both told everyone that they had sex because she didn't know what else to say, I was the first one she told that it was an attempted rape; and yes her parents are now informed but I don't think any legal action will be taken). Then later in October she and I began dating, but not officially until November. Less than a week before we officially began dating she messaged one of the guys she used to talk to wanting him back and wanting a future etc. (I found this while playing with her iPod several months later, innocently as I wouldntve even checked what it had she not repeatedly lied that she didnt talk to him after September). Now here's where the real issues begin. While it would simply take too much time to tell the entire story suffice it to say that she had lied to me countless times about this and things surrounding these things. Last week she made me feel completely worthless for not believing her about something I soon after found that she lied about. At that point I said that if she ever lied or omitted anything again then it was over, and she said she never would again. Come a week later she tells me about the attempted tape and her sexual escapades with her cousin (which she lied about countless times until she just came out and said it, no I wasn't heavily questioning her or anything. Now my question is should I stay in this relationship where I am being constantly lied to? I admit that many of these things are none of my business, but since ive always tried to tell the truth, especially about my past, I feel like I deserve some re iprocation. I have done all I can to make her feel better about the sexual assault, and she's actually mostly over it, but I'd look like a terrible person if I broke up with her now (which isn't something I want to do). Now she says (and I believe her) that she feels absolutely awful for lying but the fact is that she still lied and i don't know how to make things better again, *not to mention the fact that I'm already extremely jealous about her sexual past, which is a big no-no I understand, but almost all this stuff (especially her relationship with J and the minor incest, and this of course doesn't include the attempted rape) are pretty much deal breakers already, let alone after getting lied to about them. Finally, I think it is also important to consider that otherwise our relationship has been amazing; both our families love the other; she was my first; we generally click very well.*
TL;DR got repeatedly lied to and don't know what to do.*

I'm sorry for any spelling and grammar mistakes and for the generally convoluted story, this was hastily written on an iPhone. I can fill in where I am asked. Again, thanks for letting me vent and giving me advice on what exactly I should do with this relationship.*