Hello, the way to fix this car fast is to take it to an expert. Since you are giving this car to your daughter you want to make sure is safe.
The main thing will be to put a new battery, 5 yeras is too much to last. it is on its last miles....
The other thing is to check the fuel filter, and the fuel pump and its presssure. You may have vapor lock or the pressure is not holding after you shut the car off.
There are other things that can cause this hot hard start, like low compression a defective sensors etc. If you need more detailed info don't hesitate to contactme. poeavor@netzero.net.
Pedro.