I didn't pay close enough attention or clarify; you cannot join a Windows 2012 Essentials server to an existing SBS domain. Small Business Server is basically gone as a product, and Windows Server (2012) Essentials is its successor. Essentials is not Small Business Server. Many (most) of the classic Small Business Server features have been removed. But the same "only one SBS Server in an Active Directory domain" rule applies.
So in that vein, an Essentials server cannot be joined to an existing SBS Active Directory domain, in the same general sense that you cannot have two SBS servers in the same Active Directory domain.
Sorry for the mislead.
You could of course join a regular Server 2012 machine to the existing Small Business Server Active Directory instance, as a member server.
My other points remain valid. Two or more Active Directory domains can happily co-exist in different IP subnets (VLANs, separate switches, whatever). The biggest issue with trying to put them on the same subnet (in the same layer 2 broadcast domain) will be DHCP contention.
What do you mean by "bridge" the two LANs, though? You could configure a router (or a switch with Layer 3 capability) to forward packets between the two networks, making communication possible while still segregating broadcast traffic, which automatically solves the DHCP problems.
You could also configure DNS in each network to forward queries to the other, so that machines in one AD domain could find machines in the other. And of course member machines in either subnet could be members of either AD domain and happily talk to their respective Active Directory servers across the router. But you would definitely have separate logical networks at least from an Active Directory standpoint. A user in one AD domain would not be authenticated in the other (unless they had accounts in both with the same account name and password, but that's a different rabbit hole).
You can create trust relationships between standard AD domains, but not with Small Business Server (that's one of the baked-in limitations of SBS). Etc.