You should have the right to go through the EU passport lane. This stems from the Schengen Borders Code article 10 (1) and article 2 (5)(a), read together with article 3 (2)(a) of directive 2004/38/EC.
It's not as clear cut as the rights spouses enjoy as it depends on your children being dependent on you. However, that would usually be the case for minor children living with their parents, especially if they have special needs. It would not readily apply if they do not live with you, are (non-dependent) adults, or if you were travelling alone obviously.
For completeness sake, note that all of this technically would not apply if the country you are trying to enter is also your children's country of citizenship.
All of you definitely and explicitely have the right to go through an “all passports” lane as well.
The approach I take is:
- Ask them. There is almost always someone directing people to lines. Explain your situation and ask which line to join.
- If there isn't someone to ask, join the EU line.
My experience is that officers are fine with mixed-passport families coming through the EU line. It's usually more hassle for them to refuse you than to process you. If they tell you "no you shouldn't come though here" then you know for next time.
This isn't a big deal. You won't get refused, or given extra scrutiny, just because you joined the wrong line.
You should take your children with you through the non-EU ("All passports") queue.
Some answers to the questions you linked mention that you might get lucky in the EU queue, as they don't split up families, but I wouldn't rely on that goodwill (and on their ability process people who don't benefit from freedom of movement).