How should I go about getting a POA and maybe guardianship if my wife will not agree?

I would seek advice from a certified elder law attorney (www.nelf.org).

They can help you in what you need to do to ensure that you are not left destitute by having to place her in a care facility, if money is an issue.

They can guide you on placement and what type of paperwork you need. As a spouse you really have loads of authority, so you may not need anything but, please see an attorney and don't listen to advice on an anonymous forum. This situation is far to important to trust personal opinions.

Movie,

Too late for POA but I’m not sure you need guardianship. It would be worthwhile to spend an hour with an attorney to ask these questions. You’re the husband, have control of the money I assume. I don’t think medical and care providers are going to demand legal papers from you to care for your wife.

I went through the guardianship/Conservatorship process with my parents due to some real estate issues. Lots of paperwork and a court hearing. Cost about $4000 and took 4 months and this was simple uncontested case.

She cannot confer POA now she has alzheimers, and in fact, with a diagnosed or apparent dementia she cannot give guardianship either. What has to be done now is that you have to apply in court for guardianship. If she is hospitalized for any reason ask Social worker to help as they can often get at least temporary guardianship with a phone call to a Judge. Otherwise, see an elder law attorney with your paperwork from her doctor that show her has having dementia, and apply for conservatorship or guardianship of her. She was diagnosed 4 years ago, and would have been better that she, having early onset dementia, had this all in place some time ago, but never too late to start. See attorney now and take paperwork from her MD with you.
Do you already have MD willing to talk to you, POA for her health care decisions these last years?
BurntCaregiver has posted this can be done by going only to the court with your paperwork. I am not aware of that being possible, but you may want to private message her as to how to do that if she doesn't reply to your question here.

Unfortunately because your wife is well into her Alzheimer's diagnosis, you will no longer be able to get a POA for her, as she has to be of sound mind at the time she signs it. So that only leaves guardianship, which you can file for with the courts, and ask the judge to be appointed as your wifes guardian. Your wife doesn't have to be agreeable with applying for guardianship, and really doesn't even have to know. Without any legal documents in place, you will not be able to make any decisions for your wife or about her care, so please get the process going with filing for guardianship ASAP. Best wishes.