"I love my wife."
Translation:Tôi yêu vợ của tôi.
This was a word selection exercise for me, and của wasn't even on my list of options.
It's common to omit "của" in this case. So don't worry about "của" not showing up in the word selection exercise.
I don't know if you can't say 'vợ anh ấy' on Duo. But in daily speaking, we often use 'vợ anh ấy', and as a southern speaker, sometime we say 'vợ ảnh' (ảnh stands for anh ấy, not the photo) ;)