<u>The answer is yes, you can capitalize the common name ("the Union is responsible for. . .) so that your readers can distinguish this reference from a more generic use of the common name ("union"). ... Otherwise, if it's an appropriate substitution, I'd capitalize it.</u>
'He had left the house' can function on its own as a sentence. That's the independent clause. 'before mother arrived' cannot function on its own. it is a sentence fragment, or a dependent clause