Mails sent from the work gmail come back in the personal gmail

Under Accounts in Preferences, there's a field there called "Email Address:". You can put a comma-separated list of addresses in there, like this:

Now your "Compose" window will have a "From" popup menu that lets you choose your sending address:

AFAIK, this works for pretty much any mail account type, as long as your mail provider allows you to muck around with the From: header.

There is a preference you can set so that composing a new message defaults to a specific mailbox rather than the currently selected mailbox.

Replies go from the account to which the message was addressed. I'm not sure how it breaks a tie if both of your addresses are included or copied, but you can always override the "from" account by clicking on your name / email under the subject field.

In the message composition window, there's a pulldown above the message body, on the right, to select which email address you're sending from. The default for this depends on which mailbox you have selected in the main Messages window. It sounds like you're doing this.

If you're sure the above is being done for sure, then it's possible some gmail filters or tagging is getting in the way and making it look as though the reply lands in the inbox for one when really it's in another.

I would check the webmail and see if the issue is also seen there. If it is, then you're likely not sending from the right account, even if you think you are.