How do we help belligerent, hermit grandmother?

My grandmother is 90 years old, lives at home, and no longer drives. Her house is organized, but it is horribly infested with termites and roaches (to the point that the termite wings are gathered along the baseboards, the window sills, etc) but she will not allow the house to be tented or an exterminator to come. We have attempted to reason with her but to no avail. She says it is terrible for her health and that those chemicals can't be sprayed in her house. (A Dr. told her that some 40 years ago and his words are coming back to haunt us)
She is no longer very steady on her feet and falls easily, which is a source of fear for all of us. However, she refuses to use any assistance. There is even a walker that sits in the corner of her living room.
Her eyesight is a mess, and the lenses from her glasses fell out but we cannot get them repaired because she will not come off those d*mn glasses even for a few minutes! She been walking around with only one lense in her glasses for almost a year.
She is fixated on laxatives and is constantly asking for them. She chugs milk of magnesia, prune juice, etc. because she claims she is constantly constipated. however, this has caused her bowels movements to be almost uncontrollable and, dare I say, explosive. She wears depends now, thank goodness, but the laxative abuse is NOT healthy. I've tried to alter her diet so that she is eating things with fiber and healthy stuff, but she turns up her nose at them. Her diet now mostly consists of white bread, some lunch meat, boiled eggs, apple juice, zebra cakes, and oatmeal cream pies.
Almost the entire top row of her teeth is rotted out at the gum line, but she will not seek dental care. They've been like this for years.
My grandmother has some form of dementia, but she is not a wanderer, in fact she refuses to leave her house. It's horrible to watch her fall apart one piece at a time, and refuse to cooperate to get any medical care or additional assistance in the home.
Last Tuesday we hit our breaking point. We had a Dr. Appt. scheduled, which she has known about and we've been discussing for almost two months. She'd been whining about needing to go to the Dr. My mother drove 6 hours to get down here so that we could all go together, and when we get to my grandmothers house, she announces that she is NOT going. She used several different crazy lies, excuses, etc, and when we refused to give in, she flipped her lid. She screamed, hollered, tried to hit me, threatened to throw a TV remote at my face, said she wanted to kill herself, etc. this went on for over an hour. Then a few days later, she whine AGAIN about needing to see a Dr. She fully remembered the hissy fit and cancelled appointments from two days before. What the h*ll????
So what steps do we take (my mother and I) in order to get her what she needs and ease our own peace of mind? After the tantrum last Tuesday, we feel that she is no longer capable of making healthy choices for herself. My Mom would like to see her go somewhere that would monitor her diet and keep a watchful eye on her, considering her lack of balance. Or at the very least, we would be very happy with a home health aide. But how do we get get ball rolling?
There is no POA or legal paperwork that would enable us to force her hand at this point, and deeming her incompetent would be tricky, at best. She still is aware of how much money she has, what bills are due, who we are, etc. etc. She is not completely "out to lunch" And we would like to approach this while preserving as a much of her autonomy as possible.
In a nutshell, we feel that we are being careless by standing by as we are and bearing witness to her self neglect. It's heart breaking. Any ideas or suggestions are much appreciated.