The western lands of Vorarlberg and Tirol are part of Austria, but they are only connected to Austria by mountainous pass which is not very practicable (Tirol and Vorarlberg among themselves are also themselves connected only through such a pass). Including the nowadays Italian South-Tirol in the equation doesn't change this fact, either.
The simplest/fastest way to reach mainland Austria from Vorarlberg is to go north and through Bavaria. From Tirol the simplest way is also to follow the Inn and to go right through Bavaria.
Both Austria and Bavaria are very old countries, and when they formed in the Middle-Ages, it was definitely not practical to go all the way to the mountains to carry messages, transport goods and troops from mainland Austria to it's western parts. So I do not understand why those western lands could be part of Austria, especially back then when transport and communication was much more difficult than today.