When I’m making changes / updates / tests on sites, I would edit the hosts file on my local machines to point the domains to the IP of the dev server. The A records on the actual domain are still pointing to the live website that the public sees, but for me on my devices, my websites are being served to me from an entirely different server. If my ee sites were created with a wildcard cert (and verified via DNS challenge), HTTPS works without a problem even though I’m not being served by the real IP (A record) of the live website. Actually now that ee allows self signed certs, it would be even faster to just use those on your local dev server (for new websites you have not yet created).
It’s handy because this way any changes/updates I make on dev, I can restore on the live website without any issues about URL mismatches etc because it’s all the same.
So basically, my hosts file looks something like this
After editing the hosts file you need to clear the DNS cache on your machine (and browser). I use this method on my Windows/OS X machines. I don’t think you can do this on iOS devices, but you can easily do it on Android.
Ps. If this is something you need to do really often, since your dev machine is on your LAN, I’d recommend installing dnsmasq on it, I ended up doing that today. Really simple to install & use. Now I don’t need to edit the hosts file on each individual machine, just on the machine running dnsmasq. On all my devices both mobile and computers, I set the DNS servers to the local IP of my machine that is running dnsmasq. And now on every device I use, I am taken to my dev server instead of the live server. I ended up doing this because I really prefer to see how my sites look on mobile physically in-hand, and not via the inspector tool on desktop.
I know I could use staging sites/URLs but I’d rather not deal with database migrations and things like that. By modifying my hosts file I just make a backup, temporarily change my DNS back to my local router so I can visit the real/live website and then restore. All URL paths etc remain the same, no annoying problems to fix.