Hi James, What OS are you using?
Yes, you can use multiple connections at the same time. But, as you have noted, one connection will prevail when you make connections out from your computer to other computers. Internet (IP) protocol knows about "addresses" but not "ports", so unfortunately it is not blindingly simple to have "port 80" use a different primary interface from your other TCP and UDP traffic (I assume you meant 80, not 81). Fortunately, there is wide support for "web proxies". Does your ISP for your LAN's Internet connection provide a web proxy (HTTP proxy)? If so, set up a routing rule so your computer uses your LAN for the proxy. Then, set up your Network Preferences to use that HTTP proxy. All your web traffic should then be funnelled through your LAN to the proxy. Everything else will go through your modem as usual. Or I am just daydreaming. In any case, the precise steps will depend on your OS.