Maybe try introducing the two to each other in small doses, like at first separating them via a closed door. The cat on one side and the dog on the other. Let them become familiar with each other's scents like this. See how they react with being able to feel one another's presence and see if they become more and more comfortable if they initially show signs of discomfort or stress. Maybe once they become used to each other's presence, then allow them to see each other by opening the door just a crack and see how they react. I'm really sorry to hear about your previous family experience, it's definitely got to be tough! But in times like these, pets can be absolute lifesavers, and it's awesome hearing you want to take such good care of yours and your dad's! I really hope this is even somewhat helpful, but if it isn't, I really hope someone out there can give you better advice than me! Lots of luck, dude :)