They're not, they're taking the baby on a motorcycle. I quote:
drive him to the doctor's office...
...
a car heading towards me
I swerve out of the way holding my son...
...
I wake up in a hospital
I had gotten into a motorcycle crash 3 weeks ago
but wasn't in a car?
been in a coma the whole time
So, OP drove his baby to the doctor's office, swerves out of the way while holding his son, then we find out he was in a coma after having been in a motorcycle accident.
So OP was absolutely driving to the doctor's office holding his infant son on a motorcycle.
No where in the drive to the doctor does it say he was driving motorcycle.
Then when he woke up in the hospital they told him he was in a motorcycle accident 3 weeks ago but he was expecting them to tell him he was in a car accident. Basically he woke up in our reality 3 weeks after a motorcycle accident not 3 years later in dream reality after getting in a car accident.
No where in the drive to the doctor does it say he was driving motorcycle.
Of course, because it's a green text with intentional misdirection. Nowhere does it say he was driving a motorcycle, and the wording leads us to assume he was in a car, but the revelation later that he was in the hospital after a motorcycle incident is the punchline.
I'm not sure why you're having such a hard time comprehending. The motorcycle accident he woke up from was the original accident. He was in a coma for 3 weeks but dreamt that 3 years had passed. Accident #2 occurred in his coma and not the real world. The punchline is that the 3 years were not real and he'd been in a coma for 3 weeks.
The "but wasn't In a car?" line definitely indicates that he was confused at the doctor telling him he'd been in a motorcycle crash, because the crash he "remembered" (within the coma, with his kid) was one where he was in a car.