Wife (37F) told my daughter that she wouldn’t be getting a car without consulting with me (46M) first

My daughter’s 16th birthday is coming up, so yesterday I asked her if she was ready for her drivers license test. She replied that “it doesn’t matter since she won’t be getting a car”. She then proceeded to tell me that my wife her stepmom told her that she wouldn’t be getting a car, because we couldn’t afford to get her one. This was never discussed with me prior to my daughter telling me this. The part that infuriates me is that we bought both her son’s 16 and 18 got the cars they asked for. If my wife thought it was an issue for us financially she should’ve discussed it with me before saying anything to my daughter. It’s not an issue financially for us. I make well over 400k a year. My wife hasn’t worked in years. The only form of income she receives is child support which she keeps for herself. Both her son’s wanted 30k plus vehicles and got what they wanted. Their biological father didn’t help, because he’s a bum. My daughter’s mother passed away when she was little. Daughter has straight A’s and is a track star. I haven’t mentioned any of this to my wife yet, but my plan is to take my daughter to the dealership on her birthday and let her pick out whatever she likes. I’m not going to consult my wife, because quite frankly I work long nude for my daughter not my wife. Why did my wife think this was alright? Are there other things she tells my daughter that never get back to me?