Learning about my sway back, core

On a day when I can sleep in, which is usually 6:30 a.m. Yes, 6:30 in the morning is sleeping in for me. How sad …
Anyway, Fridays I normally work from home. So I usually just roll out of bed and turn on the computer and work.
Today I got up about 5:45 and headed to the gym for a 6:30 a.m. hard core class.
Will pushes us pretty hard. But he never gives you a hard time if you take a break or just can’t do something. He will come over and correct you or give you an alternative.
The last 10 minutes or so of class we do ab work. In a lot of the ab exercises my back can only handle so much and I just can’t continue with the discomfort in my back.
So I asked him about it after class. I mentioned my weakish core (no matter how much yoga and abs I do I still don’t have a super strong core), my back issues, like my kyphosis, which is a curvature of the upper spine, and my sway back, which Will told me today is called lordosis and he also has it. (And with my my big butt I feel like my sway back is more pronounced.)
Will told me I need to rotate my pelvis while doing my core exercises. This move helps support the back. I learned this in y0ga and try to remember to do this often, especially when I am standing. It is safer and friendly for my back and core. And it helps alleviate  strain on my body and any back pain. But it never occurred to me to do this pelvic action while doing ab work.
For someone with a sway back rotating your pelvis puts it into a neutral position. This Livestrong article describes four exercises to help strengthen lower back muscles and work to help correct the sway back. I have done all of these exercises in yoga and do them quite regularly.
I plan to try this move in my abs class tomorrow. It is definitely needed more in some exercises than others.