jb,
I am guessing that the car seat is not leather,
car seating materials are by nature very robust and can take all kinds of hammer and most products thrown at it, this includes cleaning solutions.
My first and likely solution would be carfuly remove using pog, be carful not to wet surrounding area as ink spreads like wild fire, a number of cotton buds would be good idea because the amount of ink that will be removed will amaze you, could take an hour or so. then simply extract as normal.
Have you tried to extract in the normal way?
geoff