Must I marry a second woman to appease my mother, who will be angry with me if I don't, especially since I am already married and happy in my first marriage?

Allah Almighty has made it obligatory to honor one's parents, treat them with kindness, and obey them in what is right. However, it is not part of honoring them for a man to divorce his wife to please his parents, or to marry someone he does not desire. A person should combine honoring his mother with keeping his wife, and he should apologize to his mother, honor her, and treat her kindly.