"Don’t worry, dear. I’ll soon have the car ... again"

Please have a look at this:

=> Which one is correct? the answer is A but I don’t know why…
By the way, the meaning of this sentence is a bit weird. Do you think so?

Many thanks,

Hi Nessie

Option (A) is just fine in the sentence. It does not sound weird at all.
In the context “going” basically means working/running/functioning.

You might say that the sentence means “I will soon cause the car to start going (functioning) again”. In other words, the result of what I do to the car will be that it is soon going/running/functioning again.