I would suggest a child or family psychologist, not psychiatrist. And it would not hurt to go just to one appointment to get an evaluation, even if to simply reassure you that this is normal, albeit awful, 2-year-old-behavior.

I think the recent divorce and moving could be part of it. Did you also change daycares? Has she had a change in caregivers at daycare?

Try to be consistent with discipline. And maybe instead of smacking her bum, just give her a time out - somewhere away from distractions where she can just "chill out" for a few minutes. Ignore her completely while she's in time out. Sometimes that can help diffuse the situation.

And yes - try positive reinforcement too. When she sits politely or stays quiet or does what you ask, say "thank you" or "good job" or "that's a big girl" all the time. Positive reinforcement is often a lot better than discipline.