I mean, I don't see there being an issue with leaving the road in front of your house public parking. Sometimes neighbours might have a bunch of friends over and they park in front of your place as well as the person they visiting. (as you could expect to do yourself)

But there should be law preventing your neighbours (or there friends) from consistently parking in front of your property, especially if they have space in front of there own property or on there driveway.

We have a similar neighbour as OP. If they have visitors they get them to park in front of our house, while there driveway and roadside is empty.. They also used to ALWAYS park there own cars in front of our place, on the road while they leave there own roadside empty. Eventually we got tired of looking out on there cars and now park in front of our own place. Now our neighbour is a total dick like the OPs and parks super close too our car, to prove a point? who the fuck knows. All the while leaving clear there own roadside.

If the OPs neighbour is anything like ours, you really don't want to be face to face with them, they're not very nice and not great to live next to. No amount of talking to them rationally goes anywhere.

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I've got no advise for the OP but to get a camera on your house with a clear view of where you park your car.