All of the scenes we see with Louise and her daughter are flash-forwards, not flashbacks. We see them first in the film to subvert the cliche of a tragic loss motivating a female character or coloring all of her emotions. The twist is that those scenes are the last part of the narrative, not the first.
It's implied that Ian was/will be her husband. In one of the flashes she implied that she told Hannah's father that she knew Hannah would die of cancer and that he didn't agree with how she handled it by not altering events to change the outcome. Only Ian would have really taken such a thing so seriously because he knew more of her experiences with the heptapods than anyone else.

Ian was her (possible) future husband. I feel like they kind of left it up in the air whether or not she decided to let that future play out.

He was her husband after the arrival, she was seeing the future