unless I import the root cert file that cloudflare provides.
Are you using Cloudflare for content distribution? I helped implement Akamai to globally host our web sites some years ago, so please bear with me, some details are fuzzy.
In our case, the OurCompany.com DNS name was "owned" by Akamai and the IP resolved to some Akamai server depending on where on the planet the user was. Akamai then used a different name and certificate (I think) to access our web servers to pull static content, and route dynamic (ASPX) requests.
On the IIS01 machine check the IIS bindings and see what SSL certificate is assigned to the site. In order for your internal HTTPS to work, the site on 10.0.0.50 would need to use the IIS01.mydomain.xyz certificate.
It sounds like your site has a private Cloudflare cert assigned to it. I'm not a DNS expert, but to get that site to work internally you would need to route the IIS01.mydomain.xyz name out to the Cloudflare IP address.
I think you could use 2 different HTTPS bindings to the site. You would need a second IP address. Have one IP set to use the Cloudflare cert and another IP with the internal cert. You should ask Cloudflare for help on setting that up.