Personally, I would re-arrange the clauses in the first sentence and modify one clause for stylistic reasons (the original does make sense). There are a couple of syntax errors in the second sentence and I don't think the use of proper nouns is justified.
"If accepted for a post at your school, in addition to teaching music it would be great if I could teach a few mathematics classes. Otherwise, I am still willing just to take up the post of music teacher."
- For Teachers