They are called relative clauses. There are two kinds: restrictive and non-restrictive (also known as defining and non-defining). This explains it quite well: http://www.oxforddictionaries.com/words/relative-clauses

please help!

Thank you none the less!

Forget what I wrote. I misread the word 'emphatic' as 'empathetic'. My mistake.

The first sentence is vague because you use 'she' in both the objective and subjective position. This doesn't work because 'empathy' requires a different subject and object, because 'empathy' means to be able to understand and feel the feelings of 'others'. So, you should write something like, 'She was empathetic that her sister wanted to be in the orchestra.' for example.