Sideways king studs!
You have several issues: 1) seismic or high wind area where you live, 2) loads on wall, 3) wall finish 

1) If you live in a seismically active area or a high wind area you’ll want to take special care by using steel clips like a Simpson A34 clip top and bottom. (However, your house has been there long enough without damage, it probably doesn’t matter.)

2) To me, a king stud runs from sole plate up to top plate. A trimmer runs from sole plate up to header. So, there are two kinds of loads in your wall: vertical and lateral. All the studs need to work together to resist these loads. 

The trimmer, whether turned sideways or not, will support the header and loads based on its area and length. If the header is strong enough with one 2x member, then your trimmer is sufficient too. However, if it’s more than 10’ or so, it could buckle without being braced mid span. Bracing can be by toenailing to the king stud. 

The king stud is also holding up vertical loads, but is also resisting lateral loads. One way we insure walls act “together” is by fastening them together with clips or plywood or OSB board. Your house is too old to have these, but could have boards nailed to the wall. If so, keep them. 

3) The wall finish can also tie the studs together. Often they used lath and plaster, so the lath acted as the tie. 

One interesting thing about your house is that interior load bearing walls support more load than exterior walls, because the floor loads come from both directions resting on the wall. Whereas the exterior walls have load from one direction.  (Even roof loads on exterior walls are less because older homes are “stick built” so roof loads transfer down through interior walls too.)

I’d toenail the studs together AND insure the wall finish extends onto the new king stud and jack stud WITHOUT a nearby joint. (If your ceilings are more than 10’ high or the span onto the wall is more than the rest of the house, I’d see an architect or structural engineer.)