Need help with SQL Server 2014 and disaster recovery
Typically people just have an AG node in their DR environment and do not transfer VMs there (for some of the reasons you noted + more). You should read through the documentation for how AGs work, especially planned manual failovers for when you need to switch node roles.

You could also look at SQL Server replication to replicate your data (even close to real time). It work with DNS and even though the DB is not read only per se, you can set user privileges so they don't modify anything.  The only thing to check is it requires the tables to have a primary key. This could be a good option for your reporting requirements.

Can you consider an upgrade? SQL Server 2016+ has Distributed Availability Groups, which could really solve most of your problems. With Windows Server 2016 you can have cluster nodes from different domains. Your AG would not require it to be in the same domain or network and you can even mix SQL Servers. Read more in the documentation for Distributed availability groups.