Okay, maybe I understood your question wrong, you want a proxied subdomain on Cloudflare to be only accessible from a certain IP range (home network) correct? And all other IPs should get blocked?
This sounds like complex setups, I first thought about recommending WAF rules for this, but they might not be powerful enough. I'd recommend to look into Zero Trust and how to setup an app inside this framework (it support a gazillion way to for authentication/authorization) -> https://developers.cloudflare.com/cloudflare-one/setup/
Not trivial, but also not extremely complex, I got a demo working after an hour or two. Read the docs, experiment, learn the lingo. There is no quick way. This stuff is a bit complex by design.