I cannot give you any specific grammar rules, but maybe I can clarify the structure and some general principles. In German as in English, main clauses have Subject–verb–object order.
I hear the rain.
Ich höre den Regen.
However, in German the object comes before the verb in many (all?) other contexts:
What do you like to do? — To hear the rain.
Was tust Du gerne? — Den Regen hören.
Now we have this sentence:
Tina will .
have to
be
invited
The verb of each line refers to everything below it. Have to what? Be invited. (Not the best English, I know.)
This is the same sentence in German:
Tina wird .
müssen
werden
eingeladen
The verb of the main clause comes before its object, all other verbs come after their objects.
While I think that this should already clarify things, how would a German parse the following sentence that you suggest?
* Tina wird eingeladen müssen werden.
Well, according to the above, that would have to be understood like that:
Tina wird .
werden
müssen
eingeladen
This would be like
* Tina will will must invited.
or
* Tina will be must invited.
So, should you ever want to express that, you now know how to do it ;)