A picture would help. Sounds like a load bearing wall, so some reinforcement is likely in order.
Cheers, Wayne
Sorry for the delayed response. I had a couple other dragons to slay. I've mostly wrapped up this drain replacement. Here I'll try to tie up a few loose ends.
We used a 2" hole saw to vertically enlarge most of the holes that needed to be vertically enlarged. The existing holes were 2". We positioned the hole saw by fastening a sheet of 1/4" plywood (with a 2" hole already cut through it) to each stud as we enlarged it. I'll be installing some stud shoes for reinforcement.
One of the studs had neighboring studs too near, so that there wasn't room to accommodate a power drill. So we couldn't use the hole saw to vertically enlarge the hole through that stud. Instead we used an oscillating saw (multi-tool) to make a squarish enlargement.
I was wrong when I said one of the 2x4's of the king stud was cut off. There is a jack stud nailed to the king stud. So the drain pipe was passing through three 2x4's nailed together in one place. I've attached a picture with the camera resting on or near the sill plate. The pipe shown is a water pipe, not the drain pipe (which is higher up). After taking the picture, we cut maybe 6" off the bottom of the jack stud, so that the drain pipe only had to go through two 2x4s. We put a couple new nails through the remaining part of the jack stud for reinforcement. [edit: I'm still not sure I'm using the term 'jack stud' correctly. Anyway there were three 2x4's nailed together, and one of them did not go all the way down to the sill plate.]
We did use Fernco rubber couplings to join copper to PVC (for both the drain and the vent). Picture attached.
Thanks for all the help and the replies. The key decisions were to 1) replace the bad 1-1/2" copper with 1-1/2" PVC while giving a standard 1:48 slope to the new PVC, 2) use the flexible couplings to join new PVC to remaining good copper, 3) use a plywood guide to position the hole saw to raise the tops of the holes through the studs, 4) use the oscillating saw (multi-tool) on the studs that the hole saw couldn't reach, and 5) use stud shoes to reinforce the studs at the sites of the enlarged holes.