Why don't you just increase Vehicle Restrictions Aggression in the options?
Parking AI feature not related to it at all.

I'm having a similar issue with restricted vehicles using a street despite aggression set to "strict" just now. It's ambulances in particular that I'm trying to prevent from using a particular street, and I'm not sure if they have greater ability to ignore restrictions. It's happening inconsistently: sometimes vehicles will obey the restriction, sometimes they obey it for two out of eight segments, and other times they ignore it completely.

Also, pathfinding seems weird. Vehicles are ignoring shorter paths with lighter traffic flow and no restrictions of any kind (vehicle or turning), but are choosing to use the street that I don't want them to use or to travel wider than necessary.

Screenshots saved here:
https://1drv.ms/u/s!Am67sRov1zI0kV_EYtespMOv37y1?e=LleCCG

screenshot 1 = vehicle driving past several shorter paths, choosing to use a street (highlighted yellow) that is restricted.
screenshot 2 - vehicle obeying the restriction but taking an unnecessarily wide path to destination.

I suppose I keep getting tripped up by the restrictions not being restrictions, but more like suggestions in the current implementation. I already had the aggression at High, I'll make it Strict and see if that helps. Thanks.