By placing your Wi-Fi interface which supports packet injection into monitor mode, you will be able to issue deauth (deauthentication) packets.
Deauth packets can be crafted via the Aircrack-ng suite. This can be done by the following:
aireplay-ng -0 1 -a 00:14:6C:7E:40:80 -c 00:0F:B5:AE:CE:9D wlan0
which instructs interface
wlan0 to send one deauth packet for the following AP and client, as instructed with the MAC addresses.
With this in mind. Different OSs respond differently to disconnecting from a Wi-Fi network. Some may automatically reconnect to the last network, while others may automatically connect to a recognised network based on signal strength. If the signal strength is the scenario, then this became very simple. The signal strength of your Pineapple Nano must be greater than that of the Wi-Fi AP. The signal strength is based on where the client (the neighbour's laptop) is situated. Merely having the Pineapple Nano closer to the client will cause it to reconnect to the Pineapple Nano's public (rogue) network instead of the private Wi-Fi AP.
Such that, if the client's signal strength for the Pineapple Nano is greater than the Wi-Fi AP, then the client will connect to the rogue network, else the attack failed.