Meiheichi Teisa: Where does it come from, where do you get it from, IOW, why should they be better than you.
As far as who’s right, that probably depends on the level of inconvenience to both parties. If it’s really not that hard to all in and out with two cars in the driveway, and/or it’s really difficult for the neighbor to find parking, it would be the “neighborly” thing to tell the next door neighbor to allow the across the street neighbor to park there, although the NDN can do what they please.
If the level of difficulty is similar, that’s when I say “Meiheichi Teisa”. Although you can be the good one and be “mevater” (give in) anyhow, for the sake of peace and to be a tzaddik (tzaddekes).
Either way, the neighbors don’t really have a tayna, but that’s normal human nature, and you should understand that.