Honey - stop reading this right now and pick up the phone! Call that director/owner - get a meeting today. Lay it out on the table. I guarantee you the director or owner does not want this going on in their school. Kids have imaginations, of that I know, but they do not make things like this up without some basis of truth. Your job is to find out what that truth is - is it exactly as your daughter describes? Or is there an embellishment of the simple, understandable truth?
What you expect them to do about it is to take your concerns seriously and investigate them. Taken at face value, the situations you described, are against state licensing regulations. You can most certainly call the state up and file a complaint - they'll send someone to investigate - especially the spanking incident. There would have been witnesses - even 3 year olds can be witnesses. I wouldn't take that approach just yet, though - I would sit with the director and just be honest, "This is what my daughter is telling me is going on. Can we look at this together and determine if it is happening? And if it's not happening, can you help me figure out why my daughter would say it is?"
But you do need to do something today. What if it is happening? You need to get to the bottom of it lickety split. I know finding another daycare is hard, but what would be harder is finding a way to justify to yourself why you left your daughter in a bad situation. You are the parent here, you have a responsiblity to figure things out for her and keep her as safe and happy as you can. Let that be what guides you- and make that call now.
I wish you lots of luck with this - I know it's a tough situation (I've actually been in the exact situation before, and my only regret is that I didn't speak up sooner.) You hang in there, and go be an advocate for your daughter!