is it possible to use AAG with two 2-Node Clusters across two datacenters?
Simply put, if you have, or can create, a Windows Server Failover Cluster setup across the data centres as a stretch cluster, then there is no reason why this is won't be possible. The fact the DC's are geographically dispersed is irrelevant. Good networking can bring them together as if they were not. 

You could also do this as a SQL Cluster, with replication across the disks, and the disks presented to the cluster as a shared cluster resource.

I think you need to read up on the Pro's and Con's of each solution, and maybe speak to a Windows Server and/or Networking professional.