Instead create a whole new folder just for the photos you want to sync on the iPad. Create the albums you want as subfolders in this main folder, and place copies of the photos you want in them. In iTunes select the new folder, and if you want to be able to turn specific albums on/off also select the Selected Folders option (it may be called something slightly different).
This is a bit of a space waster, but unless you are syncing massive numbers of photos it probably won't matter, and it keeps your originals organized as you want, and safe from accidental deletion just because you were rearranging things.
The other option is to go with a third party photo organizing app like Photo-Sort or Photo Manager Pro. This won't eliminate the need to store some photos in the Photos app, but it can solve your album organizing issues for most situations.
If you have a Mac (which from your description I'm guessing not) sync with iPhotos for the best results in the Photos app.