We currently have two domains, domain1.com and domain2.com
There are Google Apps/Email accounts for each domain.
I would like to migrate the accounts from domain2 over to domain1 so that when you're signed in to account@domain1.com you can send and receive messages from both domains.
I have done this before with my personal gmail however never domain-wide with numerous accounts.
Is it even possible to map all of the addresses like this without having to sign in to each individual account?
You need to migrate the all data (more info). The email portion of the migration (unless you use a third party tool) will be the only part that will be done at an admin level. The rest will need to be done on a user by user basis.
Once you've moved added the data from domain2.com > domain1.com, you need to delete the Google Apps account for domain2.com and add it as a secondary domain or domain alias for domain1.com. If you don't want uses to be logging in with user@domain2.com and only want them to send/receive as @domain2.com, an alias will likely be the best. Info on adding one of these can be found here.
The final step will be setting up a send as on each account so they can also send as their @domain2.com addresses (they'll automatically receive if you add as an alias). These instructions can be found here.
Good luck!