First off, thank you for caring enough to make a positive difference in your parents' life. You would not believe how helpful you are being, just by caring.
Now for the hard news. It can take people decades to realize this, but you can't make anybody do anything. People will always do what they want to do. You can affect their reasoning. You can help them want to stay together. You can use force and threats to help them want to stay together (this is what people often resort to when "making" someone agree with them). In the end, no matter what, they will do what they will do.
Divorce is not something parents consider lightly. It is extremely painful for everyone: not only you or your mom, but it is likely excruciatingly painful for your dad as well, even though he is the one asking for it. It is very likely that, if your dad is talking about it, the idea has so much momentum you are unlikely to stop it.
Consider that divorce is two things. One part is legal: there are a set of legal rights that husband and wife have. The divorce paperwork will end that. Fortunately, those legal details are probably not very important to you at your age. We can basically ignore those at this time.
The other part is the social part: the relationship between your parents. I'd venture to guess that this is what you really care about. The legal issues of dividing houses and finances are plenty, but they are usually not what sends aware young adults to stack exchange to ask for advice. You want your parents to stay together. The good news is there is something you can do here.
Try to help make it easier for them to repair damage. Make it easier for them to talk to each other. Try to make it easier for them to develop a healthy, respectful unmarried relationship. There are many degrees of relationships, not simply married and not-married. They are going to have to figure out their new relationship, and you can make that easier on them. You should seek to support them.
This does not have to come in the form of direct actions. Yes, talking to them helps (especially once your dad talks to your mom... don't break the ice until they're ready for you to talk unless you're really sure you know what you're doing). However, there are dozens of little things you can do. Even little things like being good about doing your chores and being easy to work with will have huge effects. You can't make your parents stay friends, but you can choose to make it as easy as possible for them to choose that way.
Now for the real secret to this approach: it's not just specific to recovering from a divorce. It's also great for supporting your parents if they don't get a divorce. It's also great for trying to help your parents resolve issues so they don't need a divorce. In all situations, trying to respect your parents and make their lives easy always helps them.
If you try something to force them to stay together, like threatening them, all of your energy is being devoted to stopping the divorce. If the divorce happens anyways, all of your work is destroyed. However, if you seek to be a positive influence, working with your parents, the story looks better. You help them choose to not divorce (by reducing stresses on them, giving them more room to resolve their issues). If they divorce, you have set yourself up to help them figure out what their new relationship is. If they work through their issues and don't divorce, you've set them up to have a better life as a family. No matter what they choose, your good work will support them!
Others are free to disagree with me here, but I find there's a paradoxical result here: the more you show that you'll support your parents no matter what they decide, the less likely they are to divorce. It seems natural to think that the best way to keep them together is to put your foot down against the divorce, but the opposite approach actually works better. If they are to dodge the divorce, they are going to have to resolve something between them. It's something hard to do, or they'd have fixed it long ago. Knowing that you will support them no matter what they decide will actually help free them up to try to resolve their issues.
Think about it like homework. How well can you concentrate on your book report when you know you have Math, History, and English homework, plus a quiz in Chemistry? Most people's mind gets frazzled when subjected to deadlines like that. Now imagine if your History and English worries were lifted, because the teachers realized they'd put too much on your plate. "If you can't finish the homework because you're too busy on book reports, that's okay. You can finish it over the weekend." Just think about how much easier it is to concentrate on the book report now. That's what you can do to help your parents. Work with them to make sure they don't have to worry about you, and can focus on healing themselves.