the two are same aged

[Tarheel]

It was because I didn't know any other way except this.

When my son was born, we bought this new car

That would make sense if you were talking about a car that was new now. But you're not. That's why I changed the sentence to "When my son was born we bought this car new"(not used). The car was new when you bought it (the same year your son was born). It isn't new now.

[Tarheel]

Similarly, if you had bought the car when it was two or three years old you might say

We bought the car used.

[emsr2d2]

The problem of the word order could be solved by using "a" instead of "this".

When my son was born, I bought a new car.
When my son was born, I bought a used car.