Finally! I have a method that work for opening the Control Center almost every time with my Otterbox Defender.
It is actually all in the amount of touch pressure.
In other words, if you try too hard... you'll never get it or you will frustrate the **** out of yourself.
Here is the key, if you use a SUPER LIGHT touch, it works! You don't even have to get your finger all the way to the bottom. Just take your finger and do a "Feather Like "swipe from the bottom of your screen and the control center will pop right up!
I struggled with this forever until I realized I was just trying way too hard.
Give it a try and let me know if I'm crazy.