Why does my girlfriend feel awkward about me spending..?

time with my 19 yr old ex-stepdaughter? I don't include my GF and she gets upset. I took my step-daughter to a concert with one of her friends and GF got upset because I didn't include her but I took my step-daughters friend and didn't tell her. I text message my step-daughter on my lunch breaks at work and my GF gets upset. There are other examples, but the latest is I was going to take my step-daughter on a day trip and she (step-daughter) asked if her boyfriend could come and I told her I didn't want to feel like the odd man out and that I don't want to compete for her attention. I also explained to her that that is why I don't take my GF with when we hang out. My GF seen the text and got upset. Am I wrong? Should I be including my GF?