I have a Griffin Survivor rather than a Defender, but I've found that it's easy to bring up the Control Center once you're used to it. You have to put your finger just right, at the very bottom of the screen, and then flick upwards briskly. Works every time. Just takes practice.
The Survivor has a steep bevel around the edge of the screen and this can make doing anything along the edges a challenge. However, so far I haven't found anything that I can't do at all. I assume the Defender is similar in this respect, so don't give up.
Sometimes I also see a little tab appear at the bottom of the screen that seems to invite me to open the Control Center. However, I'm not sure how the phone decides to display this tab, but it might also make things easier.