Air infiltration at shed roof attachment on house

My 1990 house has a vinyl back wall, and an office that protrudes beyond the main back wall, with a shed roof style low sloped roof. Last winter, a pipe froze within the house near the back wall. I traced the frozen pipe, and it passes parallel to the back wall over the ceiling of a first floor family room. I knew it froze somewhere along a short horizontal run 12" from the back wall, in the space between the family room and the bathroom above it, both of which are heated space. I figured it had to have serious air infiltration into that void between joists. I expected to find a wire penetrating the back wall over the family room ceiling, and I found that and worse. I created a small hole in the ceiling and used a fiber optic camera to investigate. There is a large communication between the space between the joists over the family room, and the unheated space above the office ceiling. I have the house blueprints, but neither has sufficient construction detail to show me the framing connections or where the vapor barrier should be.

I clearly need a much bigger access hole to address this, but now I need to know how it should have been sealed. There was so much air infiltration that on a 10oF night, pipe inside the house in what should have been heated space froze. On a second cold night days later, I left the cold water dripping slowly, and when we successfully made it through the night, I turned it off. It then froze again while we were at church later in the morning!

Where should the vapor and air barrier be in the diagram I show? At the outside surface of the house back wall? Not at the shed roof sheathing? I assume not the back wall inside surface. A space one joist over looked pretty good, but I could see some cobwebs blowing from some draft, so it was not sealed perfectly. What would be the best way to address this?

The vapour barier should be on the back wall of the bathroom and the ceiling of the office just behind the drywall. It should have continued from the office ceiling inside and up to the floor sheeting and ceiled tightly around studs and all framing members in there.
If you have access to the attic of the office you could add more insulation in that bottom corner. Other than that I guess you will want to open that bay and insulate and add vapour barreir.

If there is a penetration going through the wall, into the unheated ceiling space over the office, you'll need to fill it with expanding foam. It seems like someone just drilled a hole to feed that cable from the family room into the office. If you just block the cold air from coming in to that wall where your plumbing is, you should be fine.

It looked like I could see out into the unheated space over the office ceiling and its insulation. I thought the rim joist was not full height in this space like it was in the adjacent one. There was no small hole drilled for the wire to penetrate, as I had expected, but a very large gap the entire width of the joist space. It was hard to get the fiber optic camera to go where I wanted it to go, but I am pretty sure I was looking out into a deep void. If so, I might be able to fill the huge gap with spray foam, but I wonder if I would be better opening a large hole in the ceiling, and sealing the void with a full size blocking piece of wood where the rim joist should have sealed it.

Not sure what you are talking about , soul plate. When looking toward the office attic you should see backing for the drywall if the floor joist is parralllellto the wall and then a full sized rim joist sitting on the outside edge of the wall. If the floor joists are sitting on that wall you should just see the rim joist. Either way there should be no void there.

It really depends on how the office and its roof were constructed. The exterior wall sheathing may just stop where the office roof rafters are attached to the house, or they may have just cut out some of the sheathing between where the rafters and the ceiling joists are attached to the wall.
I would probably give serious consideration to cutting a larger hole in the office ceiling so you can see what the issue is and either patch the sheathing or stuff a bit of fiberglass insulation up there to cover any opening in the wall.

The more I think about it, the more sense it makes to cut an access hole in the office ceiling. Once through the ceiling, I may have access to the entire space where the shed style roof over the office joins the back wall. Then I may be able to repair the sheathing across the entire width of the office, since I anticipate there will be many joist spaces with large holes. Insulating the office ceiling once I am finished accessing the space might be challenging.

That is the way I would go.. Whe you cut the drywall stay a few inches away from the wall. Easier to repair vapour barrier afterwards.