Sql-server – Can a query whose execution plan uses parallelization use the cores of a processor on a another server that’s part of the same Availability Group

This is easiest to explain if you think about having multiple Availability Groups in your environment rather than just one. Each AG listener would have its own name and IP, and it could be failed over independently to either physical node.

In that environment, there are a few different parts:

• The physical nodes - each of which has its own IP address
• Each Availability Group listener - each of which has its own virtual name and address, and fails over back and forth between the nodes depending on who owns that particular Availability Group at that moment in time
• The cluster's management point - which also has its own virtual name and address, and can be different than the AG listener.

See, one of the nodes has to own the cluster. This becomes more and more important as your cluster grows out - for example, to multiple physical nodes rather than just two. That cluster manager keeps control of the cluster's state, which nodes own which moving parts, and so on.

All Windows clusters - even a simple 2-node, 1-AG setup - have this separate name and IP address for management. Most of the time, it doesn't matter who owns the cluster, but in a multi-node cluster (say, 3 nodes in your primary data center and 2 nodes in your disaster recovery data center) where you want to get down to last-man-standing as things fail, then it does start to matter.

One of the requirements for AGs is that all instances are participating nodes in the same WSFC. I believe, based on what youa re telling us, is that the 3 instances are, in fact, in 3 separate clusters.

I don't believe that what you are trying to accomplish is possible.