Complicated photo-motion-timer switch design?
If you don't want to deal with making an electronic circuit, you could consider using a "delay on break" time-delay relay for the indoor switch. These are available in various control voltages and delay ranges -- and many can directly switch 120 VAC. (Some time-delay relays are multifunction devices where delay-on-break is one possible setting.) Cost is likely around $50. You may also need a small box and DIN rail to mount the relay.

A standard motion detector for outdoor lights can provide the motion-detection function.

The trick is wiring the time-delay relay contacts in parallel with a motion-detector output so that either the relay or motion detector can turn on the lights. At the very least, the motion detection must be a three-wire type (neutral, line, switched output) -- but it wouldn't surprise me if some motion detectors are fussy about another source energizing it's output.