Promiscuous mode is an Ethernet-level concept that should allow you to see other devices' data frames, but data frames are just one of several types of 802.11 frames. To see the other kinds of 802.11 frames (management, control, etc.), and possibly to see 802.11 headers, you need to use what's known as 802.11 Monitor Mode.
Then again, the EAPOL-Key frames used for the key handshake would be data frames, so if your 802.11 card/driver properly implemented Promiscuous mode, you should still be able to see them.
Another thing to be aware of is that 802.11 devices often transmit unicast data frames at the highest rate that the transmitter can transmit at, and that the receiver can receive at, given the technologies the transmitter and receiver support, and the RF conditions between them. So if your AP and the target laptop each have, say, a 3-stream 802.11ac card (capable of 1300mbps signaling with 80MHz-wide channels), and you Wireshark laptop only has a 2-stream card (only capable of rates up to 867Mbps), then you won't be able to capture any of the packets sent using 3-stream signaling.
Or if your AP and the target laptop are close to each other, where they can use their top rates, but your sniffer laptop is farther away where it doesn't get the signal-to-noise ratio it needs to successfully receive those signals, it won't see them.
Even if you put your sniffer machine halfway in between the AP and the target laptop, if the AP and the target laptop are doing beamforming, they beams they form may be taking paths that exclude your sniffer laptop.