So as I understand it, you have created a one-way Windows trust so that DOMAIN ONE trusts DOMAIN TWO. Given this, you should be able to assign permissions in DOMAIN ONE to objects in DOMAIN TWO.
To make DOMAIN TWO\me an admin on a computer in DOMAIN ONE, do this on the computer (assuming the computer is running Windows 2008, the procedure is very similar on 2003):
- Launch Server Manager from Start/Administrative Tools.
- Expand Configuration. Expand Local Users and Groups. Click on Groups.
- Double-click on the Administrators group.
- Click Add.
- The 'Select Users, Computers, or Groups' dialog box will open. Click on the Locations button.
- Select DOMAIN TWO from the list of locations and click OK.
- Enter the username of the user account in DOMAIN TWO (ie me) and click the Check Names button to make sure that name resolves properly to the right object. Click OK and then click OK again to close the Administrators group.
Given your first comment above about not being familiar with trusts, my guess is you just haven't ever used the Location button mentioned above but that's how you tell Windows you want to select users or groups from another domain so hopefully that helps?