the defendants wife right?

exactly what happens that night and how she did it

Not the defendant's wife, his fiance. And what happened (best as I can figure out) is that she confronted the hospital director over something to do with the defendant's medical records (covering a screw-up in surgery?) and he strangled her with the lamp cord. After he strangled her he stuffed her in the ramen cart because Minuki's panties were in the exhaust of his car, so it wouldn't start. He took her to the river in the cart when he saw the defendant. He was about to explain everything (concerning his surgery from some months back) when she woke up in the back of the ramen cart, gun in hand (quite stupid of him to leave in her hands, but whatever). She didn't actually suffocate when he choked her with the lamp cord. For some reason she didn't want him to hear the truth about it so she shot him from inside the ramen cart after the panty thief yelled at the two of them. There are some finer points of the motive that I'm unsure of, though.

Just a few more details:
The reason why she visited the doctor was to get the previous medical records that stated the bullet surgery failure with HER signiture on it.