If she is paralyzed on one or both sides from the
stroke, then the same thing could be happening with the throat muscles. If one or both sides of the
esophagus is paralyzed or weak from the stroke then the foods and/or liquids that she takes in could go into the lungs instead of the stomach, causing what is called
aspiration pneumonia. They don't do a g-tube without a barium swallowing study to see how her throat muscles are working or not working. If she could swallow, then they would say if her food should be whole, small bites, pureed and/or thickened liquids (and how thick...honey-thick, etc). A speech therapist would determine what she could or could not swallow.You could be harming her by going against
medical advice.
Some people also have a g-tube when they can swallow but are refusing food (due to alzheimer's, etc where they don't know they are hungry or
depression , where they want to die and not eat). These people can sometimes eat, but don't eat enough, so that is why they will put in a g-tube.
I can't see how they can tell that the stroke was 4 days ago. It may be possible. If there was neglect or something, then you could try medical malpractice attorneys, the medical board or the state bureau that does the checking on nursing homes and cites them for deficiencies, neglect, abuse or malpractice.
If you are her POA, then you have a right to see any and all of her records, including hospital records (records department)...nursing notes, surgeon's notes, medical test results and lab results, etc. If she is alert and oriented, then she has a right to see them.