I don't know where you stand legally, but I doubt it's a good idea for you to try and get your parents to spend time with each other and go out as a family. It might just result in your parents arguing and result in lots of tension.
What is important that you and your sister try and maintain a relationship with your mum, in my opinion.
It must be a very difficult situation for you all. In some ways I think it might be harder to go through this as an adult or older child than if you are younger. At least if your parents are separated, and you can adjust to a new childhood and to some extent be shielded from much of the detail.
Your mum should be contributing something financially to the care and support of your sister. I'm not sure at the age of 21, if she legally has to provide financially for you, though. I'm not sure what the situation is for adult children, though.
I don't know if your dad has sought independent advice or not, but if he hasn't he really needs to do this. If money is tight, and he is unsure where he stands, the CAB is perhaps the best place to start. He needs to make an appointment with the Citizens Advice Bureau as soon as possible, in some areas, it can take a week or longer to get an appointment with the relevant person.
Things are probably going to get worse before they get better, you might well be facing the upheaval of moving and there might be lots of stress for your dad involved with sorting out the financial aspects of the divorce.
However, once this has settled down, things might become easier and once you've all adjusted, I hope you and your sister and dad are happy. Remember, things won't always be so unclear and difficult.
Good luck. 