I can log onto two characters at one time on the computer, but it is not an easy task. Usually I can't only get the two to work together just long enough to trade.
First, on your mule do whatever you need.. enter codes, earn credits from games, buy stuff, trade, etc. Then log totally off.
I log in my main person through vmk.com and use the Advanced Mode to select the place and instance I want. Then, using the link in the Players Guide, I log on to my "mule." Usually the screen will come up plain black or like frozen - this is when I hit refresh (F5) tons of times until I see the VMK symbol. After the "mule" is logged on I quickly go the the same place and instance I chose for my main person. Switch screens and have you main person initiate the trade. Switch screens and have your "mule" accept and start entering all of your items. Click accept, switch screens and click accept by your main person. Immediatly close the "mule" window when the trade is complete (this may save you from having to log on again - because it's guarenteed that having both screens up with eventually freeze the browser and you will get the "Not Responding" error).
Now - sometimes you freeze and get the "Not Responding" error before you get to do anything with them. Close out of all your browsers and repeat. This requires some patience and could be frustrating, but it's worth it for me!

MsSharkBait (oohhaha)