The Major wasn't very close to his brother. No one in his family even called him when his brother, Bertie, died: the Major "missed saying goodbye to his younger brother" (3.15). At the beginning of the book, Bertie's widow, Marjorie, and his daughter, Jemima, are the biggest source of conflict for the Major. The Major wants Bertie's gun, one of a pair of Churchill rifles promised to him by their father. But Bertie didn't put it in the will, instead saying, "My wife may dispose of any and all personal effects as she deems fit" (4.59).
Well, Marjorie and Jemima want to sell the guns. Jemima pretends to be defending her mother from people who "try to walk all over her" (7.57), but the only one doing the walking all over is Jemima. Her one goal is to get the guns together and sell them so she can have a chunk of the cash.
This issue is never quite resolved. The Major gets the gun to show to Ferguson, but he accidentally drops it into the ocean. Oops. We last see Marjorie at his wedding to Mrs. Ali, but she doesn't seem to approve of it.