My husband and I have something similar. Our daughter, whimpers and cries hysterically when we'd take her to school. She goes into complete hysterics when we pull in the school parking lot. What I did was put together a list of songs from her favorite TV programs: Bubble Guppies, Paw Patrol, NCIS, and some other TV theme songs. I start it when we leave the house all the way to the school. She calms down enough to get us to the parking lot of the school and I take it with us so she hears has she runs to class. By then the teacher and assistants have her puzzle and breakfast ready at her table.
It took some time for it to work. however, her crying faded out and the whimpering still happens but not as bad.
We also let her bring a toy or a book with us. She'd play with the toy or look at the book. Another thing is we would change the route every now and then on getting to a specific place.
Don't feel bad we'd the same way when we were driving.
Hope this helps. We're in this together.

My son is almost five but he did similar awhile back but that behavior seems to have ended. In our case, he knew the route he wanted to go and pointed us in the right direction but it wasn’t always where WE wanted to go so that’s when he would have screaming fits in the car.

Thank you very much for your response. I appreciate it a lot.

I will try with the toy option and see if it helps. Regarding the songs, my son isn't much interested in watching TV or IPAD and the I can not try that option. I have recently tried the soothing autism soundtrack (from SPOTIFY), but it didn't help that much.

During the ride, he sits in his car-seat right behind the driver seat. May be that's bothering him as he can't see me when I am driving? May be I switch him to the right side (behind front row passenger seat), not sure if that will help.