Is it possible to set up a reverse redirect for mail?

Question

Email

Hello. Need some advice on the right path.
Given: domain mail ([email protected])
Problem #1: It is very inconvenient to use it via adm.tools on hosting. I want to move it somewhere.
Reality: the rest of my mail is on gmail (several). Convenient interface. I want to have everything in one window, just switching accounts.
Problem #2: I don't need a corporate account with domain mail on Gmail.
What can I do? - Set up regular gmail-mail in the style: [email protected] But at the same time, leave the original [email protected] mail everywhere (what would be written to it), and the mail redirect (on the hosting) transferred all letters to gmail-mail (which is convenient for me).
Question:it is clear with incoming letters, but what about outgoing ones? Is it possible to make it so that when sending from [email protected], recipients receive letters from the [email protected] domain mail? Like a reverse redirect.
Why do I need it? - I want to keep purely domain mail (with configured anti-spam features), but use it through a convenient interface in one window. At the same time, putting all sorts of extensions and tracking the status of sent letters (came / opened).

Answer 1

Problem #2: I don't need a corporate account with domain mail on Gmail.

You can set up mail for your domain at least on Mail.ru, at least on Yandex.Mail - everything is done free of charge and elementary.
The mail interface will be the same familiar one.
Well, if you don't want to, then:
Of the minuses, the gmail.com address will be used as the return address
Can.
By running mail on your domain.
Gmail supports this.
Still it is possible - by setup of the e-mail server.
That is, it will send to its mail server, and it will already do a "redirect".
But I wouldn't bother so much.
Why do I need it? - I want to keep purely domain mail, but use it through a convenient interface in one window. At the same time, putting all sorts of extensions and tracking the status of sent letters (came / opened).
If you transfer domain mail to gmail.com, you will have one window.
You will only need to switch between accounts (domain mail / personal mail) in the upper right corner.