If you sit on the roof of your car when you go to work, it's correct.
If, like the rest of us, you sit inside the car behind the steering wheel, you would say
I always go to work in my car.
When talking about modes or transport, you can use by
I always go to work by car
I always go to work by train
...note that there's no "my" here, because we are talking about a mode of transport not a particular vehicle.
X at Y means X is a place, and Y is close enough to X that if we wanted to find Y, we'd first have to find X. A place is large amount of space where things can be built or where things can happen.
X in Y means X surrounds Y, either physically or logically.
Buildings surround you, so when you enter a building, you are said to be in it, and can say you work in a building.
Businesses sometimes aren't just a building or room in a building, they have a campus, etc. Or maybe they have multiple buildings. So then they can be elevated to "place status" and therefore you use at.
I work in a kindergarten.
You're saying there's a room or building labeled "kindergarten" and that's where you work. If it's part of a school or greater institution, this is proper to say.
I work at a kindergarten.
You're saying there's a place called a kindergarten and you work there. This gives the impression it's a separate building, with it's own parking lot, etc.
Best Answer
It is, "The place where I work." To include "in" in the sentence would require changing it to, "The place in which I work", which is still correct but less idiomatic.
What may help to decide whether you need the preposition as in the question, is to use a variation of the basic sentence, such as answering a question:
Then the alternative construction including "in" starts looking strange:
The latter grouping becomes more difficult to say, and often this can be a clue that it is not correct, or at least not idiomatic.