Should I break up with my girlfriend? She refuses to stop talking to her ex.

Hi there- Im 32 years old and I am dating a 48 yo woman. We dated for probably 5 months before becoming serious. I stay at her house every night. I cook dinner and go to her kids games with her. I'm pretty much a all around good guy.
Either way when we 1st hooked up she was seeing a biker guy and was having trouble getting over it. To make a long story short, I was christmas shopping (When we were just dating) and she had her ex over for an hour or so. She admitted that they had kissed. I went nuts and we parted ways for a couple weeks. So then I took off to Havasu with soem other girls for the weekend. (Didn't sleep with anyone) Either way when I got back she called me and came around saying how she missed me and that I was the one for her and all that stuff. So we get back together. 4 months totally good. (I thought) This morning I was driving to work and she had left her phone in my car. Ladies and Gents I couldn't help it!! I had to know if there was anything going on. So I found text messages that she has saved from this guy that were sent last year. I also found a message saying "I've been thinking about you too" from the guy. Should I beat the breaks and bounce on this one?

Thanks in advance for your help.

XO
SB