A good question.
A local answer.

Use the current train timetable to compare your actual daily trips; either centre can be visited from the other.

Cottesloe and Scarborough use different transport combinations; check Transperth for each exact beach entrance.

Treat any light show as a separate current-schedule check rather than relying on an old forum report.

For wildlife and an island feel, allow a full day or overnight for Rottnest and arrange transport ahead.

Pick the outing that offers a comfortable day for the younger child even if animals are less visible than hoped.

Choose a destination by the experience you want: coast, wine region or a slower town stay.

Check the wind, rain and ferry conditions close to departure. A light shower is different from an unpleasant exposed island day.

Perth Underground and Perth Station are connected but serve different rail lines; allow time to walk between platforms.

A departure from central Perth adds river travel and may reduce island hours; check the timetable against your cycling plan.

Base near a useful rail line and group city, Fremantle and beach days rather than changing hotels repeatedly.

Make it a half-day with one main stop and an easy train back, leaving room for a spontaneous find.

Use Transperth's current planner for the Perth-to-Fremantle route and today's fare method; old prices can mislead.