I'd be extremely disappointed, too, and, actually you do have a right to be angry or upset...but at the situation or at yourself, not at your mom. Your parents stipulated upfront that you may use the car as long as your mother doesn't need it. It doesn't matter when she notified you she'd be returning home; it doesn't matter that you said you plan to use their car during your vacation. She wants to be home and, unfortunately, that cancels your option to use their car since she will need it. You gambled on being able to use their car during your vacation and counted on your mother not returning during that time. Unfortunately, since your father has a business trip that would leave your mother alone, she decided she'd rather be home during that time. I realize you don't have the money to rent a car or borrow a car from anyone else, but that's the fault of your planning, not the fault of your parents.
In the future, I'd have an acceptable back-up plan. I speak from experience, and I've been in your shoes (regarding relying on others in order for my plans to work). I'm actually in the middle of having a few back-up plans for the logistics of my wedding because I don't trust some of my family members to back out at the last minute (like who something will be assigned to and how DM will get here if YS doesn't show up after all, which I'm anticipating and figuring I won't be told until the day before). I also used to suffer from depression and would get pretty upset from the disappointment after really looking forward to various plans that didn't happen because of the lack of participation of others. I learned to stop and ask myself what would happen if these things didn't happen or what would my other options be, and now I don't get so upset.
All said, I'm really sorry things are working out this way for you. I hope your alternate plans are just as good.