What do you see as the difference between "This will always be your home," and "You're always welcome at my house"? Said by the same person.

I seem to be an unreliable flake, though, so I'm not entirely sure there's a finger to be pointed.

To me, they mean entirely different things, so if they said both of these to you, that's very confusing. One means you always have a home there, the second that you are welcome to visit, but not make yourself at home or outstay your welcome.

yeah, two different meanings here too. "This will always be your home" = "This place is also yours" vs "You're always welcome at my house" = "You are a (welcomed) guest to this place."

I am massively discouraged with everything.

They're very different things. One of them implies you'll always be able to go there and it will be a home for you, the other suggests you're invited back to their home but it is not your home.

It'd be hard to know without context, however.

Agreed. It feels like a context issue. Also, while they sound different to you doesn't mean they are different to the speaker.

Human beings sometimes suck at communicating.

The difference seems to be simply that between "your" and "my." Conflict within the speaker. Did they go too far w/ the first statement? Backpedaling? Or just annoyed w/ you for something and next time it will be "You again?"

Speaker could mean the same thing by them both. Without context it’s impossible to say

Context is being kicked out. Gently, but kicked out.

I'd take it to mean that if something goes wrong and you need to get on your feet later, they'd be willing to help you to an extent and want you to visit/be a part of their life.