here is a simple setup. The home router is also modem/gateway and has its own DHCP server. How do I get the home router to recognize the network 10.0.0.0/24, it does not have the possibility to enter static routes. Ping is possible in the 10-network, I can ping the outer interface on the router but nothing comes back from the home router. Which setup would work?
Many home routers will only directly support a single, or possible two (2nd for wireless), 192.168.x.x/24 networks; possibly that's your case too. (One reason for supporting only one or two /24s, as a /24 supports 254 host IPs, it's often assumed this is sufficient to support a home [or small business].)
Your 1841 may be capable of NAT/PAT. If so, you can have your 10.0.0.0/24 network behind a 192.168.x.x. IP supported by your home router.