Ok, I've been mulling over a proper reply for this thread, and I guess it's time to give it a go.
So we understand you correctly: You are using software VPN, and some websites notice this. You think installing a DDWRT device for an "always on" VPN connection will circumvent this. This is not correct, either way...the source IP seen by the website will be the VPN services IP.
Second, accessing VPN and local LAN simultaneously. Software VPN's typically have some kind of setting that enables split tunneling. For instance, I use PIA VPN, and the setting is called "block local lan". With this setting disabled, I can access my local lan, but WAN traffic is still over the VPN.
This may not be something that's part of the DDWRT config.
To answer your last question: Yes, you can config a DDWRT device for always on VPN, and use a second NIC to access your LAN. I recommend configing the second NIC with static IP and no gateway so your OS is pushing all WAN traffic out of the VPN.
Note, this config is essentially setting up two routers with dhcp, ensure the main router and DDWRT are giving out different LAN IP ranges altogether.