You (or the sharepoint admin) would need to give access to the users in Domain2.
The users are stored with the security ID's, so changing the domain name in the database would not work.
I know that you mentioned that you know it is not a good idea, but please remember, more than just being a bad idea, it also makes your environment unsupported, if you change the values in any SharePoint DB using any other means than SharePoint UI/OM... So, if you open a ticket with Microsoft Support, you will have to revert back to the latest backup that was intact ! This is a perfect example for the probabilty of messing up security completely by modifying the db values directly. :)
If you are migrating the users completely from Domain1 to Domain2, and the users will not exist in Domain1 anymore, you can use a utility to migrate all the users. Check SMigrate if you are on SPS 2003 as a starting point.
Hope it helps