How many accounts do you have? Windows, Linux or both? What type of database requirements? Any geographic location requirements? Disk and bandwidth requirements? Budget?
I second the call for the above info. Also, while there are certainly many hosts who don't brand their cPanels, you should definitely ask any host you're interested in about this prior to signing up, or at least make sure they have a money-back period so that you can get a refund if the cPanel turns out to be branded. Unbranded cPanel hosts also mean you can give your clients access to the extras without them knowing who it is you're reselling from.
Anyone familiar with a good program out there (other than renting a server) that would allow my clients access to all the extras with them knowing the name of the phantom host?
If you're thinking of installing something on your 1and1 account, I doubt that there's any such solution. As said above, you could find a reseller account with some other host. There are also what I call "reseller programs", where you sell predefined hosting packages. Typically these are closer to an affiliate program, in that you have little control over what you're selling.
I suggest you change your host from 1and1 and search for a better alternative. I don't know if its true because I have never used them before, but i've read some bed reviews about their services! Good Luck!