Looks like a list price of $65,600 ( http://enrollment.rochester.edu/financial-aid/undergrads/ says $65,344, but your travel cost is probably higher), with a net price of $12,000, which would be quite a stretch to cover with federal direct loans plus work earnings (and it looks like your low income family would not be able to contribute much if anything).
Have you checked Rochester’s net price calculator to get an idea of what its financial aid will be like with you without the scholarship?
Is the extended length of attendance the reason that her financial aid ran out? If not, do you know why it ran out for her and whether the reason could apply to you if you take the CC-to-state-university route?
What west coast state? The various west coast states have different prices for CCs and state universities, so it would help others help you if you mentioned it. If you are a California resident, the CC-to-state-university route is probably a more viable choice from cost and selection of majors than if you are a resident of many other states.
It looks like Rochester is a stretch financially, but you have not given enough information for others to help you determine whether your CC-to-state-university option will be more or less expensive.