Yes, I am very sorry to say that your gecko does not have a high chance of survival after that description. The most humane thing will probably turn out to be to have him put to sleep. If your father will not pay for a veterinary visit, then I recommend you contact a local reptile rescue, explain the situation to them, and give them the gecko so that they can get it immediate veterinary care....it is the humane thing to do. If there is no local reptile rescue, then contact your local humane society. The gecko is obviously in great pain, and suffering, after such a serious and probably terminal injury. No animal deserves to suffer in pain that way. He may hang on for a long time with very serious injuries, but he will not recover from what you have described on his own, if at all--that is a virtual certainty.
I also recommend that you do not get another pet until/unless your parent agrees to provide proper veterinary care for it if it should become ill or injuried, or you have made enough money that you, yourself, can afford veterinary treatment for it. That is a sad thing, but if you truly love these animals, you will understand why it should be so. To fail to provide medical care to an injured pet is considered neglect, in some cases animal cruelty, and it is illegal in most states in the US...subject to confiscation of the animal by animal control/humane society, and possible fines.
Alas, adults are not perfect, and that includes parents. Your father probably does not consider a reptile to be a feeling creature...many people don't. You may know better, but if you are a minor, there is little you can do about that. You could work to change his attitude, but with his wallet at stake, there is no certainty of your being able to do so...and it would not be in time for your gecko. You should also educate yourself, so that such an accident can never happen again--a leopard gecko is not a pet that should be carried around in a car loose, and your parents should have made certain that both they and you knew that ahead of time. It's not responsible for a parent to give a child a pet without doing research on its care themselves...many children are very responsible, but they often trust the adults around them to know what they are doing...and that isn't always the case. Many of us have heartbreaking stories of losing reptile pets when we were children, and the reason is that neither we nor our parents knew how to care for them. As children, we expected our parents to know, or the pet store owners to tell us, all that we needed to do to care for them, and they did not.
If a parent will not provide transportation for you to relinquish the gecko to a rescue or humane society, you may be able to get a local humane society or animal control to pick it up--simply call them. I am a parent, and wouldn't normally suggest a child go around doing things behind a parent's back, but in this case, there is a living, suffering being involved, and the behavior of your parent is both immoral and illegal, though it may not be deliberately so. If they won't drive you, call the humane society on your own. That may sound harsh, but it is the truth. Be sure to explain the seriousness of the gecko's injuries, so that it will receive immediate veterinary care when it arrives at their center.