Replication on Always On
You can't have two Distribution databases. Put the distribution database in a Failover Cluster Instance that way it is highly available.

Maybe one day MS will allow the distribution database to be in an AG. I hear you can have an FCI on a cluster that also has AG (having both on the same cluster but completely distinct instances - so two standalone instances with an AG and one FCI), though I've never done it, and probably wouldn't recommend it.

Clustering is how you make the distribution database highly available. So if High Availability is important for your organization and you need replication, then you need to learn Failover Clustering and setup an FCI.