Surely one of the wonderful things about business trips is that you just may be able to wrangle a vacation before or after in an exotic location. Since you are there anyway.
While you want to recoup the business expenses, it is important to seperate business and pleasure. Here are a few guidelines (not to be used as expert advice).
Business travel may need to be established as the primary purpose and any vacation is simply incidental. If the personal days exceed business days, the reimbursement of your air ticket may be prorated.
The actual cost of a compact car rental will be reimbursed for the portion of the trip that´s official business. When a rental invoice includes days of personal use, the total will be prorated after working out which days are for personal use and how many days are business use.
When personal travel days occur before the business event, reimbursement for lodging and meal and incidental expense (M&IE) reimbursement will start on the first business day.
Take that vacation, you need it. And get a good accountant to help later.