Drawing the plans to scale showing true wall thicknesses will help in working out these details. I think a local architect would benefit you greatly especially with dealing with a remodeling. They may be able to suggest a way to achieve an even greater way of achieving privacy in the spaces.

Here's one that I like the best. It has a smaller closet, but it solves the issue of privacy and views into baths/bedrooms. Might glimpse a bit into the bedrooms, but not as bad. Ignore some of the additional doors that don't belong. The only doors into the bedrooms would be from the hallway.

Of your two options, I like the first one best. You could have the bedroom door open on the wall by its closet. There won’t be any furniture there anyway, so let it double as the walkway into the bedroom. Does that bedroom require a queen bed? Is it for guests or for a child?

But I like lyfia’s hall to the two bedrooms and bath best. It defines the private areas of the house well.

Lots of wasted space in both. Unless that "back door" goes to a private patio or balcony it should not be there. If it is removed the walk in closet could be moved there allowing the other bedroom to have their own walk in closet. Neither of the drawings provide any privacy other than in the bedrooms. Another suggestion is to move the laundry room to where you show the mudroom even if it means moving the door unless you live in a warm climate or the outlets will be on one of the inside walls.

I too would suggest an architect but at least a rethink of moving the bedrooms to the other side of the house. Moving the bedrooms would allow direct entrance from the mud room which I am assuming is the main entrance of the house into the living room and removes the back door from entering any bedroom.

I really like what @lyfia did to make the master also have privacy. It was something I didn't like about the previous plan.