There should be some local support groups in your area for individuals faced with cancer or have family members faced with cancer. You should start with the American Cancer Society, they will have information on your local support groups, and if there are none in the area through American Cancer Society, they will and should know of others through different organizations. Maybe once you get this information you can call a coordinator of these support groups and let them know your situation. You would be soooo surprised how helpful and generous these volunteers, and cancer survivors can be for you. You may even be able to hook up with someone over the phone to give some support that way since you have kids.
I know it's hard asking for help, but you may want to see if you have a neighbor or some friends that can watch your kids while you attend a support group once a month. They are usually an hour or two, and it really might be helpful for you. And when your father is feeling better, you all can attend these support groups together.
I am sorry you have to be in this difficult situation and to have your children be involved as well, makes things even more difficult. I am sure there are days when you feel like breaking down and you can't in front of a 4 year old. I pray for strength for you, and you will get through this. My only advice is to find some time when you can to focus on something that makes you feel good (mentally) b/c you need the strength to get you through parenting as well as being a support system for your mother and father. Good luck with everything and just know there are plenty of people out there who are willing to help, you just have find them.