I went through a similar thing - my dad was terminal and I was at the end of my professional exams to qualify. It's difficult to give an answer that will you help but my only bit of advice is...think about what your dad wants for you and try and use that as a focus to move forward. Your dad will want you to have the best possible life beyond this and this is the start of that for you. As difficult as it is, try allocate quality personal time to create memories during this time too. 

As a college and university tutor, please don't think that you have to 'get on' with it. Let those who need to know (college) know what is going on, tell them how you feel and that you have absolutely no idea how it might affect you. No one does.   then just do your absolute best. You may find that with a bit of pressure off you do as well as you would have done otherwise. Ask the scholarship team to keep an open mind here; I am sure they will as much as they can.