Tennis shoulder exercises, for me, are a short add-on after lifting: band external rotations, a face-pull or band pull-apart, and less overhead volume the day before I play. I am describing my routine, not diagnosing yours.
Golf practice at home should be about 80% skill work — putting, short chips, slow-motion swing rehearsal — and about 20% a short strength add-on you do twice a week for 15-20 minutes. The skill work builds the feel you can't get at the range in 45 minutes; the strength work protects your hips and thoracic spine and gives you a little speed. The moment your home golf work starts feeling like a second full workout, you've crossed the line and it will start eating your actual training.
Golf fitness at home during a busy week means a shorter session, not a skipped week. I keep the rotational block and cut the heroics so Saturday is still a golf day.
Strength training for golf, the way I run it, is 2–4 extra exercises after the main lifts — rotation, anti-rotation, single-leg. I do not run a golf-only plan.
A golf workout at home does not need a simulator bay or a full rack. I spend 15 minutes on rotation, anti-rotation, and single-leg work between rounds. The gym work stays the gym work.