I hope you'll forgive my making some assumptions about your mother and for some of the details below.
The DNR form means that a decision has been made in advance that cardiopulmonary resuscitation (re-starting your mother's heart if it has stopped) either would not work or would not be in her best interest. It does not mean that any other treatment (transfer to hospital, antibiotics, etc) should be withheld.
When the heart of an elderly person with dementia stops, it is almost never because of a reversible process in the way that sometimes affects a young/healthy person. It is almost always because they have died.
Nevertheless, without a DNR form, the care home have to dial 999 and the paramedic crew are obliged to begin CPR. A common scenario for us in the Emergency Department is to receive a frail elderly person that was found to be dead when offered breakfast in the morning but - in many cases - died peacefully hours before.
Despite having been dead for hours, CPR has been started. They are wheeled into hospital by strangers, naked, with a tube in their airway, a broken sternum, and lots of broken ribs. The hospital team take over from the paramedics - trying to get in needles, taking blood from groins, etc. A senior doctor finally gets a chance to appraise the situation (frail, elderly, medical problems, dementia, care home) and makes the decision (with other members of the team) that should have been made long ago, i.e. that continuing CPR is either futile or not in that patient's best interest.
Occasionally (e.g. if the patient only died recently) we briefly get their heart started again with drugs and shocks. They sometimes become conscious enough to understand where they are (in a frightening resus bay with an artificial airway and surrounded by strangers). When their heart - almost inevitably - stops again, they experience dying for a second (and sometimes a third/fourth/fifth/sixth) time until someone that's experienced/mature enough finally says "stop". The survival to discharge rate for these patients is very close to zero.
In the best case scenario (the team make an early decision to "stop"), the dead patient's body has been put through a horribly undignifying process. In the worst case scenario (brief return of heart function), the elderly person has been denied the opportunity to die "peacefully in their own bed", which is what most people truly want when asked.