Can I use three-conductor #2 cable for a 100A subpanel if I add ground rod at the subpanel?
Just get the correct stuff and run it -- anything else you do's going to be a way bigger pain in the arse

Since you (presumably) have not put the wrong cable in the ground yet, your best bet is to simply get the correct cable (one with 3 insulated wires and bare ground) and run it.  If you can't return the incorrectly purchased cable, just toss it in with the next load going to the metal scrapper in your area -- you'll at least get a little bit of money back for it that way.