I think you may be confusing resolution with dynamic range. Your HDR shot is not going to have any more resolution than an ordinary shot will have. The HDR image will be large because of the increased bit depth, but you can't use the HDR file directly, it has to be converted back to 8 or 16 bits, when (as you have discovered) its the same size as a regular shot at 8 or 16 bits from the same camera. Print size will be the same from the converted HDR file. The benefits in this process are in preserving highlight and shadow detail.
You can only use HDR with tripod mounted shots. You should not have an alignment problem if you do.