If push comes to shove, you gotta have your priorities straight and do what you gotta do. As @Grant said, family comes first but be prepared to pay the cost.
For you, it means accumulating the personal days, vacation days and using only so many sick days as strictly necessary - You're going to need all of them. It also means sparing no effort to build up the cash reserve and keeping your resume up to date. It means managing your projects and your clients so that your manager can easily assign someone to back you up and stand in for you while you are gone. And being very aggressive about taking on any project that's in the critical path because you never know when you are gone. Of course, if you about to get get on a project's critical path and family calls, don't start getting on the critical path just yet. The worst thing that can happen is family calling while you are in the middle of a critical path, and you want to avoid getting caught in that scenario as much as possible. Be ready to formulate some contingency planning involving those of your projects that are on a critical path if you are called to be at your father';s bedside. True, your management gets paid the big bucks for this but if you help them with sound thinking and judgement, they'll value you all the more as an employee.
At the moment, hopefully, the cancer is in its early stages, the situation is manageable and your family has enough relatives who live next to your father to attend to his immediate needs. Whatever helps take some of the pressure off you.
I am ambivalent about whether you should tell your boss at this stage. If your father is enough bad shape that absences on short notice on your part are necessary, then you have to talk to your management and give them a heads up. If the cancer is in the early stages, the situation is manageable in the sense that those around your father can take care of himself without requiring your immediate presence, I am reluctant to advise you to talk to the management. Because talking to the management while nothing is going to hapen for several months is like hanging a sword over their heads. If there is one thing that managers hate, it's uncertainty. I wouldn't tell anything to my management if my work is unaffected as yet and the only result of telling them is that they can't do anything but wait in anticipation for me to drop the other shoe on them.
Basically, you are in a situation where you have to manage both your personal and professional lives for uncertainty. The advice I just gave you amounts to putting as many odds on your side as possible, not worrying about crossing the bridge until you get to it and once you get to the bridge, make the decision of whether or not to cross it without looking back in regret. Yes, you need to keep your management in the loop, but when you do it is important. You are in a situation where worrying doesn't get you anywhere but where good planning might.