A.J.
These incidents are NOT related. Even if she's been acting this way ever since, her behavior is not related to that day anymore.
You need to treat this separation difficulty as though nothing bad ever happened. Because nothing did. Thank God traffic wise. Many kids go through this. She heard about strangers stealing her somewhere, that's why she is saying it.
Be sure no one did try to steal her (I'm sure you would know if you've been with her every minute for the last 2 years!) and don't put to much weight on that discussion right now, it will add more fear. And don't let her "milk it"! She simply does not want you to leave her side, and therefore is getting as upset as necessary to make sure you don't. Her fear is real...to an extent...but don't get manipulated.
It sounds like you may have subconsciously convinced her you believe this is valid somehow by still linking it to a minor incident when she was 2 in your own head. It's not a post traumatic reaction, clean the slate in your mind! You have to be calm, cool and in charge, and her security will improve. Work with the day to day "weaning" first and get into details about stranger danger later at a totally separate time.
When my daughter was about 2 and a half, my husband and I had to take a trip to LA and we left her with my parents. It was the only time in her life she's been without me. We left in the morning before the kids were awake (she has an infant brother), and I didn't warn her we were going the day before because I didn't want to upset her in advance by explaining the length of time. She was already great about good byes with no trauma. She was fine the whole time we were gone, started asking for us the last day. However, understandably, the day after we got back, I ran to the neighbors to pick something up, and my mom said as soon as I left, she started looking around wildly and panicking-afraid I would be gone for days.
I've always been very firm about "leaving her" in the gym daycare, or while I run errands, or whatever. She went through a brief crying phase but it didn't make me hesitate to leave, so it didn't last. After the trip incident, I knew we had to get right back to the norm even though her new fear was justified. I still made sure to leave and do errands etc and told her firmly and confidently with a smile and a big hug when I would be back. I didn't let her cling even though this had just happened. She got over it quickly, and she DOES NOT remember the time we left her for a few days. And it was only this past year.
You have to work up to that point. At 4, she can put up a big fight, and she's been allowed to so far. So be prepared! But start with short errands while leaving her with someone familiar like her dad. Be confident, happy, with a clear conscious, and give her a hug and walk away. Do not entertain the screaming for a moment. Tell her dad not to either. Just move on to a positive activity and let her be. But if she is having angry manipulative tantrums weeks after you have started leaving her for things and she knows you're coming right back, you shouldn't allow that, and should discipline her once you're sure that's what she's doing.
Meanwhile, keep the discussions short and positive like, "No one will steal you (ONLY if SHE starts talking about people stealing her-don't ever bring it up yourself). You're a big girl and momma has to go. I'll be back in 30 minutes-hug kiss." Done. Go. If you go no matter what every time, she will not be scared, and she will give up the fight. If you feel guilty or sad or worried, or she occasionally succeeds in getting you to stay with her by crying and being scared, it will fuel her. Be in charge. This will pass!!! Good luck, I know it's hard! I've choked back many tears once I get out of sight of my little girl when she doesn't want me to leave! Even if she doesn't cry!