Only put a female fish in a breeding trap if they are really ready to pop out babies. They will get stressed, and can die in those traps. They also need to swim around, and should really only ever be kept in there for a few days at a time. Some will be too stressed by the breeding traps and will actually refuse to drop fry in them, while some will be fine with it. Depends on the fish and the tank. Also, be aware that larger mollies and similar livebearers will sometimes eat the fry in those traps with them. They are not generally high on maternal instinct. In fact, it is usually pretty non existent.
Also, I am not sure that is a molly. I agree it look like a swordtail, or perhaps a variatus platy. That said, same behavior, and gorgeous fish. Good luck!