My girlfriend plays tricks with her ex

I’m confused.  My fiancé is working with the civil service. She buys me gifts regulalry and she keeps telling me that she is ready to marry me. I have introduced her to my mother and brothers and they like her. However, she does not want to introduce me to her friends and relatives as her boyfriend. When I complain, she just laughs it off and apologises, but she does not change.

 

One day she spent a night at my apartment and  the next day called her cousin for a lift to the village.I accompanied her to town, but she did not allow me to greet her cousin, who was with a friend. I later learnt that her cousin’s friend was her ex-boyfriend. Does it mean that they were only talking or she has not told him she is involved in another relationship?

 

Recently, I was unable to access her inbox on her Facebook account. I eventually got a password and I found a message from a man praising her as “she is hotter than other he has ever seen”, the guy also sent  his phone number.

 

I waited for her to tell me about this man, but in vain. I checked her phone and found that she had saved the man’s number. When I asked, she told me that, took the number to assure the guy that is engaged. When I insisted, she confessed that she had not told him about engagement, but they are still communicating. 

 

Will my girlfriend ever change for the better? Is my girlfriend marriage material ? 

Though we still communicate with each other, I no longer trust her. Should I forgive her? 

Tofa