You didn't need to remove the rule. You just needed to enable folder redirection on your device.
Messages > Options > Email Settings > Menu Key > Folder Redirection and then select the folders you want redirected to your device. In your case the support folder. There's no way to "send as" the support address from your device. The BES can only activate one Exchange account per device.
If your company supports OWA, you may be able to add the Support account to the BIS site. This will give you the option to receive email (to a new folder on the device) as well as send email from that account as well. However, you would need to know the password to that account to set this up.
The difference between stupidity and genius is that genius has its limits.
When you take things for granted, the things you are granted, get taken.
Even a mosquito doesn't get a pat on the back until it starts to work.
Too many people miss the silver lining because they're expecting gold.
[BES 5.0.3 / GroupWise 2012 HP2]