astrophysics - What is the orbital path of Omega Centauri?

I was under the impression the only objects relatively close to our Milky Way but not yet a part of it were the Sagittarius Dwarf and Large and Small Magellanic Clouds and then much further out, but otherwise relatively close, the rest of the Local Group.

I was reading Florin Andrei's answer to Do all the individual stars that we can see in the night sky belong to Milky Way? and was confused about the facts of Omega Centauri. Upon researching more, I became more confused:

I hope that outlines my confusion...

My question, then: What is the orbital path of Omega Centauri (illustrations or animations would be appreciated)? Is it in or a part of our galaxy or orbiting externally more like the Magellanic Clouds?

EDIT: As seen in the comments below; I see how the second part to the question may be ambiguous. So, please focus on the first part of the question (What is the orbital path).

No speculation please, only fact; especially when talking about what Omega Centauri may have been in the past.