It sounds like you have a problem with flashing between the wall and the floor. These types of leaks which are often caused by driving rains can be difficult to find. If you've identified a gap between the floor and the wall, I would seal it as best you can then see if the problem reoccurs. Sometimes you can test a leak repair with a garden house. But leaks which occur during rainstorms of a particular direction are famous for being tough to solve.
Wind driven rain can really wreak havoc on a house.
It depends upon how large the gap is. I would prefer that it be flashed with aluminum or copper. In the alternative you could try a silicon caulk. Question from Andy -Coping saw won't cope out miters of my tough crown molding. Sorry to hear you're having trouble coping with crown molding.