Is SQL Server 2014 capable of having Availability Groups set up across multiple domains? If not, is there a third party tool you can recommend to mirror a 13TB (and growing) database across domains?
No, not in SQL Server 2014.
You can have Availability Groups across multiple subnets, but they all must reside on the same domain (even if they span data centers, continents, etc). This official document states as much for Windows Server 2008 R2, but I can assure you the same remains true for more recently released versions of Windows (emphasis mine):
Windows Server 2008 R2 requires that all the cluster servers must be in the same Active Directory domain. Therefore, SQL Server multi-subnet failover cluster requires that all the cluster nodes be in the same Active Directory domain even if they are in different subnets.
And from this document (emphasis theirs):
Availability replicas must be hosted by different nodes of one WSFC cluster: For a given availability group, availability replicas must be hosted by server instances running on different nodes of the same WSFC cluster.
This is enforced by the underlying Windows Server Failover Cluster (WSFC), not AGs directly. You can't have a Windows cluster traverse domains, and since AGs need to all be part of a single WSFC, there is no way to have them span domains.
For newer versions of SQL Server and Windows there is a new concept called a Domain Independent Availability Group which you can read about here. And for SQL Server 2017 there was a requirement to support Linux, which obviously doesn't have Windows domains, and you can read about that here.
Klaus Aschenbrenner talks about setting up a Basic Availability Group in SQL Server 2016 Standard Edition and Windows Server 2016, on a simple workgroup (no domain at all):
Yes, Windows 2016 supports Workgroup and Multidomain clusters.
For Workgroup nodes and Multidomain cluster nodes should be able to ping and communicate.
and SQL server is supported including hyper-v and file server.
I tried this on my laptop by configuring between virtual machines. you can make use of this as reference. However I have not done this on production environment.