If the dog was in trouble, he'd be wet and bedraggled, he wasn't.
If you were leaving, you wouldn't abandon your obviously well cared for dog (regularly walked, suggests this) in an open area to fend for himself. He would have been left at home.
You don't leave in Wellies or crocs or whilst on a teams meeting.
If the water was only 2-3ft deep and she had slipped in the river, surely a possibility to get out nearby?
Why did family ask for 'privacy'?
Why did police not get a tracker dog in, which might help indicate direction the missing woman went in?
So dreadfully sad. Praying she is found safe and sound.