I'm inclined to agree with Ryask... I would feel really unhappy taking that amount of money from my folks, but would do at last resort. It is a really good opportunity and if you feel like you can't get anywhere with what other options you have then you should definitely take it...
I guess you could think about what other things you could do to get better at home - some of the same sort of things that they would be doing as an inpatient (maybe with some financial help from the family!!!): additional therapy / pdoc appt. What lifestyle factors could you change to help with your stability? Can you learn more about BP in general and your BP - triggers, warning signs, develop plans etc. Could you reduce your work hours to give you less pressure and time to focus on improving your moods. Are you doing therapy at the moment along with meds???