So, I would need to borrow between 10,000 and 12,500 from someone.
Not sure how you arrived at this figure. I'm estimating: $4k for lawyer $500 for utility deposits (wild-a$$ guess here) $2000 for a down payment on a $10k reliable used car (plus cosigner if needed) (maybe less if you trade in your used car, but since it's not worth much, might want to keep that for daughter)(be sure to get a car with EXCELLENT gas mileage, like a Honda Civic, with your long commute) Extra $1000 for incidentals or extra lawyer fees I'm assuming your relocation money will cover first month's rent and moving van rental
That gives me $7500. Now, if you think you can borrow $10k, it may be better to pad that a bit so long as you keep the extra in an emergency savings account. That will give you some cushion so you don't have to call your parents up AGAIN in 3 mos.
You'll have to be super mega frugal once you get there. Powwow with the girls about ways for all of you to save money/ bring in extra money. But you can do this. An extra $500/mo from tutoring, writing, dog walking, babysitting would pay your car payment and an initial loan repayment to your folks.
As for a fair interest rate - no risk CD would bring in 1-2%. High risk stock fund 7%. You're in the middle risk category, so maybe 4-5%? But if you could get them to take 3%, all the better. Ask them for 3 mos before you start payments, low payment the first year (like maybe $100/mo) and increased payments after that.