Two different Apple IDs with two different @icloud.com mails
Solution 1:
No - if you really have two different AppleID each with different @icloud/@me/@mac addressed - they cannot be merged or swapped one for the other. If you just want to use the @icloud.com to log in to one AppleID that's also known by a different email address - you can do that easily by changing the username on each device.
See Apple ID - Want to make my [email protected] primary Apple ID?
If you have two AppleID - the best you can to towards merging them might be to make a family plan and share purchases and migrate mail/contact/calendar data off the account you wish to avoid.
See Renaming iCloud mail address for that.
Solution 2:
I have a similar problem. The best solution for me was to forward the mail from the old Apple ID to the new Apple ID. This way you can migrate over time to the new Apple ID.
- Log in in icloud.com using your old Apple ID.
- Open Mail.
- Click Actions (cog in bottom-left) and choose Preferences.
- Select Forward my email to and enter your new Apple ID.
- Click Done.
You can also select "Delete message after forwarding" when you're sure it's all working correctly.
I know it's not strictly what you want, but I found it the best solution to having an old and new account.