Remote control you Mac in your home LAN while on the road can easily be done with SSH.
1. Enable port forwarding in your router of port 22 to point to the ip address of your Mac in your home LAN. Make a note of your public ip address as well, you need it for the login.
2. Enable Remote control on in system settings.
2. From a remote location use SSH to establish a secure connection:
ssh -N -L 69000:127.0.0.1:5900 login-user@public-ip-address
3. Command-K and type: