W.C.
Sometimes kids will go through another separation anxiety phase between 4 and 6. So it is no abnormal and you can relax a bit. It is a phase, but you need to help her get through it.
You need to remind her verbally that you know she is scared but you are leaving and you will be back and then go. Don't look back. Don't stay a minute longer. Don't forget something.
As far as the car thing. Have her help you do some of the things you need to do in the morning. Then put her in the car, tell her you are know that she is scared about you leaving once she is in her car seat, but you are not going to do that. Then walk slowly around the car. Do not rush...etc.
She is just more aware that you might not come back. You need to show her that you will, by going away and coming back again and again.
Good luck.