mamashtakah,
Now that I’ve asked, can you ask your Rav and let us know his reponse (rather than your assumed response of his)?
I did ask. He did not see any halachic problem with opening the door for a date, or a wife, or a daughter for that matter. He is of the strong opinion that opening the door is absolutely not chukat hagoyim. He added that he opens the car door for his wife. I asked him why HE does it, and his answer was “because it’s a nice thing to do.”