I am a non-EU citizen with permanent residence in EU. My wife and my kid are EU citizens. When travelling togehter by car, are we allowed to use the "EU citizen only lane" when crossing borders, although I am not EU-citizen?
You are entitled to use that lane, not merely by car but also in airports, etc. as you are in fact covered by the EU freedom of movement (as the spouse of an EU citizen travelling with her).
The same would not be true for another third-country citizen who would happen to share a vehicle with unrelated EU citizens (the Schengen Borders Code is silent on this, which means there is no special rule or exemption in this situation).
In addition to Relaxed's answer here are the relevant articles backing it:
‘persons enjoying the right of free movement under Union law’ means:
(b) third-country nationals and their family members, whatever their nationality, who, under agreements between the Union and its Member States, on the one hand, and those third countries, on the other hand, enjoy rights of free movement equivalent to those of Union citizens;
Persons enjoying the right of free movement under Union law are entitled to use the lanes indicated by the sign shown in Part A (‘EU, EEA, CH’) of Annex III. They may also use the lanes indicated by the sign shown in Part B1 (‘visa not required’) and Part B2 (‘all passports’) of Annex III.
Third-country nationals who are not obliged to possess a visa when crossing the external borders of the Member States in accordance with Regulation (EC) No 539/2001 and third-country nationals who hold a valid residence permit or long- stay visa may use the lanes indicated by the sign shown in Part B1 (‘visa not required’) of Annex III to this Regulation.
They may also use the lanes indicated by the sign shown in Part B2 (‘all passports’) of Annex III to this Regulation.