CFL Fixtures: one lamp stays constant, the other cycles on an off
Continual cycling of fluorescent lamps on and off was once a symptom of a bad thermal starter switch or a dying fluorescent tube, but if your daughter's house was recently remodeled, it's very unlikely an ethical contractor would have installed such a lamp.

If this is truly a CFL (compact fluorescent lamp), designed to fit an incandescent lamp socket (Edison base, e.g. E26 in USA), just replace both lamps with modern LED lamps, which are more efficient, longer lasting and less expensive, and come in a variety of colors such as this "warm white" (2700 K) model.