Don't understand why you're running two domains on the same network but that's another discussion.
If you're authenticating to a device on a different domain from the one you're currently authenticated on, you have to use this syntax in the username field: \\[target domain]\username. The username you put in the field has to be a valid username in the target domain unless you have a trust relationship between the two domains.
Also, you're committing another mistake by using public/routeable IP addresses. You should be using 192.168.x.x. If any of these domains are connected to the Internet, you can create all sorts of routing problems accessing resources on the Internet where those resources also use the 192.169.x.x address.
If you're authenticating to a device on a different domain from the one you're currently authenticated on, you have to use this syntax in the username field: \\[target domain]\username. The username you put in the field has to be a valid username in the target domain unless you have a trust relationship between the two domains.
Also, you're committing another mistake by using public/routeable IP addresses. You should be using 192.168.x.x. If any of these domains are connected to the Internet, you can create all sorts of routing problems accessing resources on the Internet where those resources also use the 192.169.x.x address.