How to vercome this problem, which problem? You mean your love for her and not accepting her past or your family wants you to get married?
Lets assume its the first assumption. My simple suggestion is, forget the past, accept the love she has for you and the love that you have for her. Unless you had that love, you wont bother about her past, right? Thats human nature, we get sad when something is done by someone we have a different expectation.
You should be happy that she trust you that much that instead of telling a lie she opened up her past in front of you. If she didnot love you, would she bother to tell anything? Can you respect that truthfulness? Rather than hearing from someone in future, she wanted to be open with you and shared her past.
These days a lot, I mean a lot of girls are habituated n premarital sex. Some can even fool their man, some knows the man was no saint. Hardly you can have a girl who is physically and morally a total virgin. Rather than accept a chance of counting on your family where a nice girl is chosen and in reality you find her a metaphorical whore in nature. Have faith on your guts and chose the one whom you really do love. Your worry on this issue clearly says how much you love her.
In a lot of countries, specially in Europe and many part of US, a lot of guys dont feel like having sex with a virgin. If a girl saves herself, that is treated as she must be having problem. Being virgin or not is a perception, if you can deal with that, good for you, if you cant, you may stay as a 40 year old virgin still waiting for the right one.
Think about the girl in a differnt way, she might have found someone as her soulmate, she opened up and had sex seeing a future, and found there is none. Later from that eperience she tried again and found the same on the second guy. Now she is counting on you and trying to be honest with her past, if you also dump her for some old faith she poised on some jerks, what is the difference between you and them? They were looking for free sex, you are looking for a sealed virgin. I feel bad about this girl, if she gets dumped for such a reason like trusting someone, then she might take some bad step in future, wont trust male in life again.
Bottom line, love is there from both of you, get married and have a nice life together.