I also have endometriosis, so I completely understand what you're going through right now.
Ryand is very correct that insurance companies can be reluctant to approve hysterectomies when the patient is fairly young and when all options have not yet been exhausted.
Have you asked your doctor why he/she is opposed to a hysterectomy?
Given the fact that you do not want children and that you also have adenomyosis, a hysterectomy will most likely give you much needed relief. But, in order to make the endometriosis become inactive, both of your ovaries would have to be removed, thus cutting off all of the hormones that "feed" the endo implants. Are you okay with a surgeon also taking out your ovaries, which would throw you into menopause? If you do that route, there are various add-back hormones which can be added in tiny doses that may help lessen the menopause symptoms - such as hot flashes.
Have you had any surgeries for your endometriosis? If so, do you know if your surgeon burned the lesions with a laser or actually excised them (or cut them out)?
The reason that I'm asking is because the excision method has proven to be the most effective at removing endometriosis. When the lesions are burned, there is a high chance that the endo will return. Unfortunately, only the endometriosis specialists actually excise the lesions. It's still very common for Ob/Gyns to burn the lesions during surgery, and as a result, the endo quickly grows back after surgery.
I don't know if you live near any endometriosis specialists. If you do, I highly recommend that you see one for a second opinion.
Concerning the Mirena implant, it has shown to be effective in some women. Only a few small clinical trials have been performed on the Mirena's effectiveness in endometriosis treatment, but the results have been promising.
The Mirena implant shouldn't hurt once it has been implanted. (You may experience pain during the insertion process though, so you may want to be prepared for that if you decide to go that route.) Women spot for about the first six months after the Mirena is implanted, but after that, the spotting lessens dramatically.
Potentially, the Mirena may help your mood swings by balancing your hormone levels. It will depend on how you react to the progestin in the implant.
I know how intimidating doctors can be when they back us into corners concerning medications, but definitely speak up and discuss your concerns with your doctor. Learn your various options and then possibly seek out a second opinion. If you still feel that the hyst is your best option after you investigate your options, then see if your insurance company will approve it. Ultimately, you know what is best for you and your body, so trust your gut instinct.
In a month, I'm traveling out of state to have surgery with an endometriosis specialist. He will be excising my endometriosis, which has implanted on my ureters and bowel. He will be aggressive in the surgery, and he actually did recommend a hyst. I chose to not have the hyst, but I am hopeful that the surgery will help me otherwise. I'm considering having the Mirena implanted after the surgery. Before now, I've had six other surgeries for my endo, but in most of them, the surgeons only burned the lesions. As a result, the endo quickly grew back - thus continuing the cyle of pain.
Good luck in getting your pain and other symptoms under control, and good luck making a decision about what to do.
Take care, and be well.