What can you do about a dementia patient who believes she has nonexistent young children?

My mother and I are caregivers for my grandmother with Alzheimer's. Over the last few months, we've been dealing with a number of problems that seem to be typical...loss of time and place, feeling she isn't at home, etc. These problems aren't too big a deal and are mostly manageable with diversion and so on. However, she has terrible issues in the afternoons (often starting right after lunch) in which she believes she has a number of children (the number and age varies) and she knows they aren't at home, so she wants to search for them. When we try to keep her from going outside unsupervised - she isn't able to safely move from place to place as she's mostly restricted to a wheelchair- she turns aggressive and nasty, claiming we've hidden her (nonexistent) children from her and occasionally takes swings at us and even bit mom one day. It's shocking how strong she can get when most times she struggles just to get out of her chair! She makes up elaborate stories around how she got these kids and what they were doing each day to justify the things she says about them. She wants to search houses that don't exist and go to places that don't exist to find them. It's impossible to provide her any proof that these children don't exist, of course, and even if you gently correct her at the beginning, she forgets and the cycle starts all over again. She's threatened to call the police, have us sent to prison and also threatened to kill us. I've caught her searching the places where her guns used to be (long ago removed.) Does anyone have any idea what to do to calm this behavior, for her own good and everyone else's? We'e tried to be as caring and loving as we can (of course it's scary not to know where your kids are) but no amount of distraction seems to work. Telling the truth doesn't work. "Therapeutic lying" doesn't work. We're at the end of our ropes here and at the point of burnout and I'm really concerned about my mother's health from the stress of all the constant fighting. This happens on most days but doesn't occur to the same degree every day; when she isn't in "that mode" she's reasonably easy to deal with. We've been to a doctor and she has medication; it does help her sleep through the night which is good, but we need some idea for how to deal with the violent and nasty behavior since the medicine doesn't seem to be acting on that. We have another appointment with the doctor but it will be months before we can get in. Is there anything we can do, or is the only choice just to deal with it and hope for the best?