A very small area of the subfloor at edge a tub has rotted, fix ideas?

So while having dinner at my mother's house today, I noticed two small cracks and what appear to be small water stain on her living room ceiling.

It was right below the bathroom. So after some investigation. it appear that at the corner where the tub met a wall, the subfloor (an area of maybe an inch or two?) has rotted. The floor is soft, and i can actually push the vinyl floor down slightly with my fingers. Which made the loose caulking in that area even worse. Rest of the edge around the tub seems to be fine. It is just that corner.

There is a small access panel which allowed me to peak underneath the tub, the plywood underneath the tub appear to look fine. I couldn't find the rotted area with my hand from the access panel either. Maybe the tub sits on a different piece of wood?

Photos I took: http://imgur.com/a/P0mS4/layout/grid

So few questions:

1. What would be the best way to fix this without taking out the tub/vinyl floor/living room ceiling. I'm going to re-caulk, but the fact the vinyl floor can be pushed down slightly at the rotted area, I'm bit worried that the new caulking I put on will tear. Should I just apply huge amount of silicon caulking at that corner?

2. Would vinyl shoe molding work better? Since it would cover the rotted area, and then the rest will be sealed with silicon caulking.

3. How should I repair the two small cracks on the popcorn ceiling.

Thanks.

Silicon works best 20' deep in a landfill, unopened.

The vinyl shoe molding is a good temporary fix, however in addition, replace the caulk at the tub-floor joint and up the wall and tub, and please use polyseamseal by locktite, it works with your finger and remains flexible for years.

The ceiling cracks do not appear to be any more serious than can be repaired with the same caulk and wiped with a sponge.

Anything you do will be a temporary fix without a full gut.

By the time you have a leak like this is showing in the ceiling down stairs, it's bad. cut some drywall and inspect the framing in the wall. If you can't get into the wall around the tub maybe the back of the wall in the next room.

Thus us going to be either a low spot in the floor collecting water, a place where shower spray ot tub splash aims at, or both. You might get by with a patch job got a year or two but this needs a fix which is going to include tub or shower removal.

I like plastic shoe in bathrooms since it's positively going to get wet. My preferred caulk for this is "Duo-Sil" by Siroflex; a paintable silicone bearing urethane caulking with amazing adhesion and good flexibility plus it lasts. When I'm doing a bath I always raise he base off the floor slightly so that even if the shoe passes water the base is unaffected. If I find base on the floor under shoe molding I cut that relief space out with a jamb saw before installing the shoe.

You have to be anal with keeping shower and bath areas caulked and sealed very well or you will most definitely have big problems ahead in your future.

Phil