[Nextgrid]

There are pocket-sized travel routers which have Wi-Fi & Ethernet ports and run OpenWRT.

You can run a VPN client on it, connecting to the outside world via Ethernet and then making an access point bridged with the Wi-Fi interface. The other side can be a VPN server (running on a similar router or any Linux PC) at your home as to appear as your typical residential connection. I wouldn't recommend using any commercial VPN provider as they could risk raising some security concerns. Given that you keep your home and internet connection, just use that. Get a cheap used laptop or Raspberry Pi as the VPN gateway if you don't have one already.

Any device connected to that Wi-Fi access point will appear as if it was on your local network (on the other side of the VPN tunnel); the only giveaway could be latency to local devices and potentially reduced MTU, but someone would have to be explicitly looking for this and running tools while remoted into your machine to detect that.

Note that modern laptops use Wi-Fi for their own location services and can detect their location based on the networks around them (the actual network names/BSSIDs, looked up in a DB as opposed to the IP given by the network), in which case you're probably better off keeping Wi-Fi off (or even physically disabling it by removing the wireless network card or sabotaging it in some way) and using Ethernet to connect to your travel router.

Regarding your approach, this is mostly fine but I'd suggest using Linux for this and lower-level tools such as StrongSwan and IPTables rather than a Windows PC and a commercial VPN client, just to avoid any potential undefined behavior where the VPN could disconnect and somehow your "fake" LAN interface gets bridged or NAT-ted to the "true" LAN interface instead of simply going dead.