• Circuit Playground VOUT --> Neopixel 5v (to one strip)
• Circuit Playground G --> Neopixel G (to the same strip)
• Circuit Playground A1 --> Neopixel IN (2 wires: one to each strip)

Power

Your battery will plug in to one end of the JST extension cable / switch.  The leads from the other end of the switch will be soldered to the IN end of your second strip of neopixels (the one NOT used by the Circuit Playground).

The two neopixel strips will also have a power and ground wire running from the OUT of one to the OUT of the other.    

Power will flow from the battery through the switch, and into the second Neopixel strand.  It will continue out of that strip and into the first strip, then from there into the Circuit Playground.  This will both protect your Circuit Playground from LEDs drawing too much voltage accidentally, and also balance the weight and bulk of the battery and the Circuit Playground between the two bunny ears.

Remember: Pixel data can only flow one way, from the IN end of the strip to the OUT end.  Power can flow either direction, so it's fine to hook up your power supply to the opposite end of the strip from your microcontroller.