If your mother lives in a nursing home, the staff is correct in saying that they cannot force her to take medication if she refuses it. However, if she needs
this medication, and due to her paranoia and distrust she refuses it, perhaps the nurses can get an order from the doctor to crush the medication or to hide it in food. They will need your consent to do this, especially if you are the Durable Power for Healthcare. Then, they can try to see if she will take the medication that way.
Some medications are made in liquid form or in quick dissolvable tablets that make them easier to give to patients. The liquid med can easily be mixed with juice so that it is easier to give. The dissolving tablets are nice because they simply have to make contact with the person's mouth and they will dissolve. In other words, they cannot be spit out or hidden under the tongue (some patients do this and then spit them out when no one is looking). This way, the staff will know for sure when the medication is given, as long as it got into her mouth.
One of the ways I will try to get people to take medications is to first reduce the number that they are taking. Many pills can be stopped temporarily, so that perhaps your mother could take only a few pills daily. That way, it is not so overwhelming for her when she gets her pill cup, and she may be more likely to take it.
I suggest working with the staff and physician to try and see if you can work something out. I would ask if other formulations of the medication (liquid, dissloving tablets) could be tried. This may take some effort and it may take several different tries, but eventually you all will find the best way to get your mother to take her meds. If all else fails, some of the meds can be given by injection. This can be tried for a few days, and once she can start taking the medicine orally, she can be switched.