"why would the home invader shoot the wife dead but only tie the husband up"
Perhaps the first death was an accident. People don't exactly behave cool headed and rational in these sorts of situations. Anything could have happened. The wife stepped up and got killed, the husband cowered in a corner. The killer realized what he did and didn't want to be in jail for the rest of his life. The killer hated women, or recognized her and knew she could ID him. Who knows.
Thats why we have courts and rule of law. 'It wasn''t me, it was the one armed man' and all that.