Ok. I am not trying to freak you out.... but um, yeah, I would not try to make a bunch of excuses for all the "innocent" things this could be.
If it were an "official vehicle" of some sort, there will either be a notice on your door from the water/cable, tree service/ whatever. Why your house and not all the houses on the street?
Sure, there is a slim chance that it was someone lost who pulled over to check their phone and it just happened to be right in front of YOUR house, but given the recent events in your life, I would over react instead of under react. Sorry.
As for trying to determine if it was your ex's car or not, I would be more interested in trying to determine enough about this particular car in case it shows up in the neighborhood again. Your ex could be driving a totally new car, borrowed one, stole one, or whatever.
Would your neighbor call and report a "suspicious vehicle" at your residence and the time? I think it is a good idea to keep the police aware of the potential for an incident at your location. Also, if there is another incident and they are called to your home, the pattern could be helpful to have documented.
I am so sorry you kids are having nightmares. It certainly sounds like they are affected. Are they in therapy? Can you think of ways to help them feel empowered?
I have experience with the nightmares. The good news is that it did go away with time. A few things my boys did: they decided to share a room so they didn't have to go to bed alone, they slept with a light on, a few times one would wake and ask to sleep in my bed. They took the dog with them. They used their ipod to listen to music or a favorite tv show to go to sleep to. (The youngest watched/listened to Johnny Test episodes on YouTube.)
Neither child was able to do sleep overs for about a year. The night fear at home was bad enough, but away from home? Nope.
I pointed out all the good people that live around us, including where I knew policemen and firemen and even an SBI agent lived. We frequently talked about all the things we do to be safe.
I like CSI and Criminal Minds type shows, but I did not watch them when the kids were at home. My oldest child would call downstairs if he heard me watching tv and he even imagined it was a "scary show."
Patience and time with the kids.
Heightened alertness and reaction to strangers and strange vehicles at your home.
If your ex reasonably expected the house to be empty, and chose that time it seems to me that he expected it was "ok" and he would not get caught but that he is still fixated.
Stay vigilant. (((hugs)))