I just found out my current family is moving out of the country so I obviously started looking for new jobs. I interviewed with a new family and ended up being offered the position that starts next week. I let my current family know right away (which was a week ago), however, they spent all of last week trying to convince me to stay. Finally over the weekend I explained that unfortunately I just can't stay with them until they move (which is in the middle of summer) and they asked that I stay through the end of next week knowing my new job starts next week.
How do I handle this situation so that I am not burning bridges?
My current family is great, but I have felt very manipulated and taken advantage of as they are consistently late at the end of every day and do not pay me for any time off, even when their kids are the ones who get me sick. They also refuse to pay me overtime even though I work 45 to 50 hours per week.