1. If you are driving your car now, come here immediately and give me a ride home.

Question

( Is this one correct? In this sentence, the driver is in the middle of driving his car. Is that right?)

2. If you are driving your car after work, give me a ride home.
( In this sentence, the driver is not driving his car. He will drive his car later after work. Later the person wants to ride the driver's car, doesn't he?)

Answer 1

Your interpretations of these sentences are correct. You could omit 'your car' each time since that is implied in the word 'driving.'

I'd also add 'please' after each comma.