Caulking and mold;
Caulking that lasts needs more prep time than the actual application of caulking.
My experience with caulking repairs is that mold typically forms in voids
* where caulking is missing,
* or has delaminated from the surface,
* ---OR if someone didn't kill and remove the old mold first before simply just gushing on new caulking!
The old caulking should be removed. ----And, running scotchbrite over the surface will show where old caulking bits still resides, even when you didn't previously see it with "naked" eye.
I've see mold magically grow BEHIND caulking.
So, I have had success first;
tsp-ing the mold,
-thoroughly - drying .. assisted by hairdryer and time,
THEN the comparitively easier part of applying new caulking.
Also, inhibit the water spilling over. There are simple over-the counter plastic-to-tile wedges in the soft form of a triangle to put on the corner of where the shower wall meets the tub or shower pan such that water would be lesslikely to drip off to the floor. If you're going to be caulking, it would be very simple to caulk that in too. Sub-floor and framing repair costs are massive. This wedge costs $5.