My toddler does not listen and idk what to do anymore

Need advice on what to do with my 3 year old daughter. She DOES NOT listen. And when I say doesn’t listen, I mean like not at all. Her father and I have been separated since before she was born and he cannot coparent well, so I know that doesn’t help the problem. Lately, she has had such an attitude and constant either ignores what I say, says no, or back talks me. Spanking really doesn’t phase her. I’ve tried time out. It works temporarily but still doesn’t fix the problem. The biggest issue is in public. She has so much energy and is a social butterfly anyway. She won’t ever stay by me and runs away, is at too far of a distance, is distracted by everything, and again doesn’t listen when I tell her to stop or to stay by me. It’s to the point where I don’t even want to take her in public. I know I have to pick my battles, or else she’d spend her whole day in time out or getting spanked it seems. Looking for advice for what to do to get her attitude back on track and get her to listen more. I haven’t tried taking toys away yet, because again I feel like it wouldn’t phase her and she’d find something else to do.