No - you should not run multiple nodes on a home network.
First, running more than one node with the same private keys on your home network is wasting bandwidth by syncing two copies of the blockchain over your download link. You can get the same results by running one node and using multiple harvesters on multiple computers. Second, if you have uPnP enabled on both nodes and your home router supports uPnP (and most do) it will cause both of your nodes to not sync the blockchain. You need to disable uPnP on all or all but one node behind a uPnP enabled router. The CLI command chia configure --enable-upnp false will turn uPnP off on a node. It requires a restart of the node to take effect. If you disable UPnP on all but one of your nodes then your local router will forward inbound 8444 traffic to the one node and the rest will now be able to connect to the network but just will not accept inbound connections from the network.