My husband is in the military and we currently live overseas. My mom has developed dementia but refuses to see a doctor. Do I wait until an accident happens to come home?

Much depends on the medical access you have for her. You could try to get her to a doctor to have her blood pressure checked or something of that nature - make it "routine".

Then, ask the clinic if there's a way that you can alert the doctor ahead by letter as to your worries about her dementia. Once in a doctor's office, she may cooperate a bit more.

You aren't alone in this. Sometimes it takes an emergency to get them in for help. I hope you don't have to wait that long.
Carol