I have successfully managed to avoid marriage for the first 40 years of my life, so I can't comment directly on "what I told my wife". I remember fondly having that conversation in the car with my male work colleagues, you know the "how many kids do you have?" conversation. I told them I had six - three cars, two jet skis, and a deck boat. Funny how much they enjoyed that.
However, I've been on the receiving end of many a woman's comments about their husbands/boyfriends, so I would offer this...
Of course, if the finances are going to be strained, she's not going to like it. This is pretty much unavoidable. Would you like it if she bought something that costs tens of thousands of dollars that was primarily for her benefit? If she happens to be a big shopper, you might be able to remind her about the money she has spent there. I've told girlfriends in the past, "you can view my tool and car part collections the same way I view your clothes and shoe collections". I've had moderate success with that. I suspect that GN prices are near the bottom of their "value curve", so if you buy a car and keep it nice, it should at least maintain if not go up in value.
What I think is a bigger concern for them is the time your car will take away from them and the kids. If they have it in their head that the car will result in you spending many hours alone in the garage, they will not support it. However, if you can show them that the car is an opportunity for you to do more interesting things together (car cruises, taking the kids for ice cream, etc.), you might have a chance of getting them to support buying the car.
It's a tough sell, even with the above arguments. Maybe you can hot-rod that minivan... A lot of it depends on the woman and what she assumed she was getting when she married you, and what her expectations are now that the kids are around.
Good Luck!