Need help creating Access Point (via Pi's WiFi adapter) and connecting to a router via external WiFi adapter

Hi guys, I need help with something I'm working on. Sorry if this is not the right sub to post this on. Also, this is my second post on Reddit (first one is in /r/raspberry_pi, so this is a duplicate of that one).

I have Raspberry Pi 3 model B, running latest Kali image (kali-linux-2018.2-rpi3-nexmon.img) and I would like to create an AP using the Pi's internal WiFi adapter (wlan0) and then connect to a router using an external USB adapter (Alfa AWUS036NH, wlan1).

I have attached a scheme of how exactly I want to do this. I've been trying to find articles and how-to's, but they're either outdated or they are for different OS versions (Raspbian, Jessie, etc).

https://imgur.com/a/c9Xzfwz (Visual Scheme of what I'm trying to accomplish)

So, basically, I want to connect from my Laptop or Smartphone to my RPi running in AP mode (hostapd and dnsmasq) via SSH (wlan0) and then connect to the router via the WiFi adapter (wlan1) and be able to see and communicate with all the clients in the network (Internet Access is a plus, but not mandatory). The AP on the internal adapter would be configured to run on startup automatically when the RPi is powered on and I would manually connect to the router once I'm logged into the AP (I'm guessing by providing the BSSID and the Passphrase of the router in the wpa_supplicant file).

Is something like this possible? If so, can someone point me in the right direction or help me set this up? Any kind of help is very much appreciated!

Thank you!