What is the rules for colonial nations taking my new colony territories?

In the New World, I have a few core territories, two vassals I wish to annex, and a colonial subject inbetween them.

I need to build a "core territory" next to the vassals to annex them, but the moment I finish colonizing a territory, it almost always becomes part of my colonial nation (I guess if it's adjacent to it?) even if it's directly adjacent to one of my core territories.

For example, in the screenshot below, "New Spain" got instant ownership of Wichita when I finished colonizing Wichita, despite my core "Caddo" being immediately adjacent to it.

A) I don't understand the rules for when colonizing a territory, for whether it becomes part of my nation or part of my colonial subject's nation.

B) How should I core territories next to vassals in this kind of situation? (I have a clear path next to the green vassal, but not to the red one)

C) If a colonial nation is adjacent to a vassal, can I annex the vassal? If so, my whole issue becomes a non-existent worry.

First of all, have a look at the map of Colonial regions and the Colonial Regions page on the EU4 wiki.

As you can see from the map, America is separated into colonial regions. The region of your colony is called "Colonial Louisiana" if I am not mistaken. As long as you have 5 colonies in a colonial region, a colonial nation will appear. Any new colonies you create in that region will be automatically added to the colonial nation.

A) I don't understand the rules for when colonizing a territory, for whether it becomes part of my nation or part of my colonial subject's nation.

As I wrote above, any new territories that belong to an established colonial nation of a colonial region, get added automatically to said colonial nation.

B) How should I core territories next to vassals in this kind of situation?

The problem you're facing has to do with the coring/colonial range. You have a few options here:

• Create a colony in a different colonial region and see if you can annex the vassal then.
• Wait for unrestricted coring range in Age of Revolution.
• Release the vassals and attack them.
• Move your capital to the new world.

I'd recommend just trying to create a colony in a nearby colonial region and see if it works.

C) If a colonial nation is adjacent to a vassal, can I annex the vassal?

Again, this has to do with coring/colonial range. Bordering the vassal with your colonial nation won't make much difference. Have a read through coring range.

Just a word of warning, if you manage to annex those 2 vassals, they will probably be added to the existing colonial nation, increasing Overextention and decreasing Religious Unity and in general greatly destabilize the colonial nation.