Is it permissible for me, in Islamic law, to divorce my wife based on my mother's request? And is it permissible for me to prevent her from opening her pharmacy due to potential harm to me, or can I seek a divorce based on my belief that she suffers from perpetual lying?

Your wife's major errors—her not accepting your family, her lying, her bad manners, and her expelling your mother and your niece—are all matters you should not have tolerated. Divorce is permissible in Islamic law if it becomes the only solution to problems, although we urge you to first try to reform your wife and mend the relationship between her and your family, and to bridge the rift with all your might. If her reform proves impossible and you cannot reconcile her continued presence with your dutifulness to your mother, then divorcing her would be a just solution, and you would not need to resort to deception. As for preventing her from opening a pharmacy, if she stipulated this to you at the time of the marriage contract, then you do not have the right to prevent her, provided that the work does not involve any Islamic prohibition. If she did not stipulate it, then you have the right to prevent her from working.