multiple email addresses

Work with your particular mail providers.

There's not much we can do, should a particular mail provider you're working with not allow a "foreign" reply-to address, for instance.

Mail ISPs usually do block unauthorized route-through. Which means you'll have to use the expected credentials with the SMTP or ESMTP server. But that's not at all unusual.

The mail provider most commonly used here does not block by reply-to address, though some others may well do that. Free mail providers are probably going to be more restrictive, and not only because they also want to receive any email responses to your outgoing messages, too.

Multiple mail accounts, each with a unique POP or IMAP read/retrieve server and credentials, and a separate SMTP or ESMTP send settings and credentials, works just fine.

I select a specific source address and don't use the automatic selection mechanism, and override the reply-to and the account when needed.

Google has available tools that allow Google to collect and display all your mail via gmail, where Google logs into your other mail servers.

Verizon acquired AOL a while back.

If Verizon is active and you're getting duplicate mails, then the accounts are not separate. Or there's server-to-server forwarding happening, and the "duplicates" here are message forwards or message retrievals.

I had “fun” with a Mail.app installation a while back, and ended up removing the entire SMTP configuration and recreating it, as the SMTP data was somehow corrupted. There are some discussions around with details of removing plists to do this reset, as an alternative approach. Had I to do it again, I’d remove it all and re-add using profiles.

DMARC has nothing to do with the mail client, unless the client is spoofing the from address and not the reply-to address. And the mail server shouldn’t sllow that.

Unless somebody has started checking mail server settings during sending—a few providers have done that—that message was likely also blocked by Verizon.

Not sure what app or web service is generating that display, either.

Here? Connection Doctor, and a review of settings. Maybe removing and re-adding.

The settings might be similar, but they’re clearly not sufficiently similar to be working the same. This is thr bane of setting up mail, and from any provider. Probably in the SMTP settings, if reading mail works.

Aware of DMARC, and have set that up on occasion with private mail servers. DMARC errors are a squabble between mail server providers, if the messages are otherwise legitimate. Clients have no access to DMARC. Not unless the client is sending a forged from address, as differentiated from a reply-to address. (Check the raw SMTP message headers to see that detail.) But again, if this works on one of the two clientw here, then the other is almost certainly set up diferently. And if this works with DMARC from one, DMARC for the other—absent the accounts behing “homed” on different mail servers, and DMARC being messed up,across the different servers—is not specific to the client.