Hi Robert – thanx for your questions!
The reality is, that swimming/biking/running is already excellent core training, especially if you swim with the pull buoy band, do the low RPM rides and especially, running hill repeats.
If you are limited on time or have extra time, it’s best to simply focus more on the swim/bike/run. 3 sports, is already a lot 😉 then by doing the right training, you can get the specific strength work while developing your aerobic base at the same time.
It’s very common, to see triathletes, develop small aches and niggles, by “hitting the gym” as it does put a lot of stress on your joints/tendons. As well to the reality, that triathlon is an aerobic sport (aerobic = with oxygen) that requires 10-20-30 THOUSAND repetitions. Versus doing 10-20-30 reps, with lots of resistance. It will also hinder your all around consistency and sensations when it’s time to nail key swim/bike/run sessions.
If you do need to get in the gym, supposed you have a particular weakness, then best to do so, in the offseason. You will also see lots of professionals do strength training, but they are trying to squeeze that last 2/3 % out of themselves, as well to being monitors by trained specialists.
Then for stretching, it can be a bit risky, and not very beneficial. Triathlon is not a range of motion sport. You don’t need to be flexible, to be a good over long distances. But if you do some stretching, keep it lite, and best to do it, when your body is properly warmed up, like out of the sauna, or hot tub.
The best way to prevent injuries and feel better is to get on the foam roller 😉
Hope this helps and all the best in your season!