+1 @ tsl - standard blinkies don't provide drivers sufficient warning + reaction time (possible exception of dedicated bike trails and slow subdivision side streets). > 1 light provides bigger visual target and reliability.

I consider PBSF and knock-offs the minimum to provide enough warning time. I have 3 on road bike (seat stays & seat bag) plus a Mars 3 (easier button action) on back of helmet. Commuter has a Dinotte 200R (lithium version) rear, plus a Portland light + reflector combo (Virginia requires rear reflectors for night) and another PBSF clone. Based on chasing another rider with a Dinotte, it's easily visible for 1/2-full mile - terrain/sight lines or weather will cut it off before light level does. Based on daughter's comment ("Dad, your lights are OBNOXIOUS"), it will get driver's attention, assuming they saved any for the road.

For your kids' trailer, a small high-power steady or flasher (PBSF clone, Mars, one of the more capable blinkies?) on the trailer flag would be an attention getter due to the whipping motion from the flag. Once spotted, drivers may use it's range of motion to judge how far left they should go.