My personal experience is that hormonal fluctuations due to my menstrual cycle aggravate my IBD. I am approaching menopause and I cannot tell you how eager I am to stop menstruating FOREVER.
Doesn't the mirena give a low dose of progesterone? Here's what the website says: "It releases small amounts of levonorgestrel, a progestin hormone found in many birth control pills." It also says only a small amount of this hormone enters the bloodstream.
Progesterone is a muscle relaxer. It tends to slow bowel function. I have no idea whether the amount of progestin in this IUD would have the same effect.
I'm sorry you're flaring. From what I've read it seems most likely that the Mirena is not a cause of the flare.