I'm not surprised to find she has a "vulnerability". Around 1/4 of the adult population experiences depression or some related mental health issue, and alcohol related issues are also common. Also, we are becoming more aware of the challenges of menopause as people live longer, enjoy better physical health and perhaps expect more out of life than our ancestors accepted. (This last sentence expressed clumsily by a man whose only relevant experience is seeing his wife suffer badly during the menopause, but whose mother says, "In my day we just got on with it.")
However, I find suicide by drowning in a river an unconvincing explanation. I've spent many years of my life thinking suicidal thoughts. The fact that I have never tried it perhaps means I am not the best person to ask about a "preferred method". However, my feeling is that, confronted with the reality of cold water on the face, and struggling for air, the body's own instinct to survive would take over. It is not easy to drown yourself without weights or some other mechanism to overcome the body's reflexes.
For what it's worth, the women in my office — self appointed experts all — are loudly proclaiming that her husband/partner has "obviously" killed her. I personally consider this to be extremely unlikely. If I had to put money on the outcome, I'd put it on her leaving (either alone or with/to a lover?) intending to contact her family after a few days, and then she's seen the publicity storm and panicked. However, I do not know the river in question, and there must be a reason why the police remain of the opinion that she has most probably drowned.