Mirena has been linked to significant weight gain as it contains hormones. Not only does it create a barrier for implantation, but it contains similar hormones that the pill does (and we all know how the pill causes weight gain!)
If you truly do have PCOS, which I would question as you don't sound as if your borderline diabetic or watching your blood sugars, have no mention of excess hair on your face and you have been successful at getting pregnant, then this could be a cause for inability to lose weight.
The smoking gun to me is the fact that you've had previous liver issues AND you have your gallbladder removed. In my practice I have realized that most people have adrenal fatigue and most have liver issues. If you can believe it, about 50% of my patients no longer have a gallbladder and are stressed beyond imagination!
When you have your gallbladder removed, it puts excess strain on your liver as it has to immediately produce bile, rather than using stored bile when you eat a meal. This is not very efficient and can cause improper metabolism of fats. This will then decrease your ability to absorb Vitamins D, E, A, K. You will then have decreased immunity, decreased healthy cell growth and and increased risk of all cancers if this goes on for a prolonged period of time.
When your adrenals become fatigued your sleep starts to get difficult (waking up at odd hours or insomnia), crave sweets or salty foods at around 10am and 2-3pm, moody, difficulty losing weight, etc.
I'm sure much of this has to do with the Mirena IUD, but I do like to get to the true CAUSE of the problem and I believe that your body has been crying for help before the IUD was put in (or you wouldn't have mentioned it in the advice request!).
You are sincerely the typical case I get the privilege of seeing everyday. If you would like some help with this and any other health issue, I would be honored to help. Please email me with any questions, concerns or information on how to make an appointment. God Bless.