"Production" and "development" could be considered as two different web sites which happened to run the same application. This means, your problem boils down to running several different web sites with SSL on the same IP address (and port).
This problem is the valid use case for the reverse HTTP proxy.
Give your sites different names (which will be used to refer to them by the third parties). For example, one could be called example.com and the other development.example.com. This is enough for the proxy to be able to distingush and route requests to appropriate server.
For running both sites with SSL, you need your reverse proxy to support SNI and install all certificates with private keys onto it. Also you configure request routing on a proxy such as example.com gets routed to production server and the development.example.com to another server. Then you have to forward port TCP 443 to your proxy.
Your software choices include at least Caddy, Nginx, Apache; there are more. I wouldn't be surprised if IIS itself could do reverse proxying; in this case you may forward port 443 directly to the production server, which runs production site and also configure it to proxy development site to the other server. (IIS supports SNI since version 8.0.)
