Do trade routes activate between my cities when a road goes through city states or other civilizations' cities?

Question

Suppose I've got a capital, a city, and a city state in between, where the dashes represent roads:

Capital ------ City-State ----- My City

The road goes straight through the city-state. I understand that I don't get a trade route to the city-state, but would I still get a trade route to my city? Or would I have to build around the city-state? And do the same rules apply if the city-state was replaced with another civ's city?

Inspired by this question.

Answer 1

Regarding passing through another civ or city-states territory:

Trade routes can pass through other civs as long as you have open borders agreement from them. Trade routes do not work through a civ you're in war with, even though technically your units can pass within their borders.

Regarding city-states, it works of you are either friends or allied with them.

Regarding passing through an actual city:

I believe it's precisely the same as the above - your road passing through the actual city shouldn't make a difference, except for saving you money, since cities count as road tiles.