A few clarifications please.
"Copied files from C drive to this new drive". By that I assume you mean you just copied files to the new drive, and you never ran XP from the new drive, right?
"After formatting C drive ..." Presumably after formatting C, you reinstalled XP from the CD back to the C partition (i.e. a fresh installation)? Or did you install XP from some installation files on the 30MB partition?
Drive letter changes. That would seem normal, after a fresh installation of XP, if the new drive has a primary partition. On a new installation of XP to the C partition, XP will start afresh and assign drive letters in the normal way. The drive letter changes you have described are normal.
If you want to change the drive letters, you can (more later), but I'm not sure it will have an effect on the way XP installs the OS updates.
"it seems to be looking to install the updates on E" Are you doing it through the Windows Update site?
Normally, Windows Update will only detect and install updates to the current operating system from which Windows Update is running (this is so even if you have a dual boot). So if you are running XP from the C partition, it should not install updates to other partitions.
Why do you think it's trying to install to the E partition (and are you talking about the 30MB partition, the present E, or the partition on disk(1), the old E?) What indications did you get which made you think it's installing to E?
You're better off clarifying what's wrong with Windows Update first before changing the drive letters. To change drive letters, Click Start, Run, type diskmgmt.msc and press Enter. Right click the 30MB partition, and select Change Drive Letter and Path. Click Edit. You cannot change it back to D immediately, since it's been taken by the partition on disk(1). So change it to any available letter (this is only temporary). Click OK. You'll be warned about changing drive letters. Confirm the action.
Then right click the partition on disk(1), repeat the steps, but now the letter E will be available. Change it to E.
Then right click the 30MB partition again, and change it to letter D, which is now available.