I'll preface my post by saying I've gone to 5 inpatient treatment centers in my life. Only two of these experiences counted for anything b/c they were the ones I undertook as an adult, of my own volition, desperately seeking stability. Each time I had no money, no job, and had lost much of my support (luckily, aside from that of my family, albeit very tenuous support). My point is, obviously, it will work best for you if you are 100% ready to relinquish your habit. The less reservations you have the more likely you will be successful. Even in my favorable episodes in treatment, I encountered impasses and dilemmas that'd send me running and crush my will to persevere had I not been determined and desperate to get clean. I had to put it above disputes w/ nursing staff about my meds (I'm a type 1 diabetic, and having external forces manage my medicine drives me up the wall, but I overcame that only b/c I knew it was important I stay there - it was that or leave and almost certainly use).
I never detoxed benzos in any of these stays, but several patients in my wing detoxed 'em, as well as alcohol. The particular setting I am referencing was in an actual hospital, in an auxiliary building outside of, but adjacent to the hospital. They had 24 hour nursing staff, doctor visits everyday, and all the amenities that usually come w/ a hospital stay. None of the benzo detoxers had complaints about their titration. Nursing staff will take a benzo kick very seriously due to its mortality risks. I think you should do your best to contact your insurance and speak w/ a clinician who can tell you what hospitals in your area offer this service under your coverage. I had to call a mental health hotline associated w/ my insurance. During your intake be very direct and specific w/ your questions: what are the detoxes like? How long do people stay on average? Can you smoke? Is there a religious aspect? What kind of doses, and all questions that pertain to your meds should be answered before you put your name on the dotted line. You don't want to work up all that courage to go through those doors only to find yourself packing up a day or two later over some petty technicality. That is a fast way to crush your will to see this struggle through to the end.
After I detoxed I went to an extended inpatient rehab program where therapy and life planning were conducted. It was very inclusive of all elements of my life to where I felt I received a holistic level of care. As I said earlier, it wasn't all perfect. There were challenges w/ staff and my family along the way, not to mention the almost perennial cravings over the first few weeks, but I put everything aside as secondary to staying in that facility until I completed the program. They made me go to AA/NA for instance, which I hated. I told myself I wouldn't do it. When I was told that was a mandatory non-negotiable part of the program, I relented and tried to assimilate as much of it as I could to my own benefit. I didn't become a big book thumper, but I did manage to cull some helpful things form those meetings. They also took away my outside literature, which I considered essential to my therapy - just another thing I had to work through - and after a week I'd convinced them to return all my books. My point is, you will certainly have to compromise and get a bit uncomfortable in a treatment center. No one wants to go to rehab and share living space w/ some other addict, and have your time managed for you like a child and so forth, but frankly, as an addict I realized that was actually kinda good for me during the fledgling days of my recovery.
Any treatment center worth its weight in salt will provide support for mental issues. They should address that aspect in group therapy primarily, and in one-on-one follow ups w/ counselors, psychiatrists, and administrative teams. By the time you leave they should be offering you a plan you should execute to a T even if you feel some of it is unnecessary. They should bombard you w/ follow up and aftercare information and opportunities to connect to a larger recovery community outside of the center, as well as opportunities for employment and other courses to enrich your life.
My recommendation is to write out a list of maybe some of the things I've said here, but definitely the things you want out of treatment and ask about each one as you survey different options. Hopefully you'll have many as you have insurance. You are extremely lucky in having access to treatment. Less than 1% of the population does I am told, and most people do it rattling in the back of 12 step meetings. I know I was lucky to have it.
PM me if you have any questions or need help making a list of things to look for so you can find the right treatment center. Best wishes.