But if you got stabbed in the gut, you wouldn't wait until the busy season is over to go see someone about it.
I want to second this-- depression is getting stabbed in the brain, and it puts all the chemicals out of whack. Yes, there is something to be said for maintaining a positive outlook, but you *must* be vigilant and make certain it doesn't turn into a blind "head-down-bum-up-just-keep-swimming" mentality, because then you run the risk of completely losing yourself.
The biggest thing I struggled with, and I think may come to play with you, is that life will *never* be the same again. This changes you. Traumatic family illness changes you, just as your children changed you when they were born. I lost my father, suffered a serious injury, and miscarried my first pregnancy all within the same 12 months--and in hindsight, I did more damage to myself, my ex-partner, and everyone around me by clinging to the idea that if I "just kept going/working/paying the bills/etc" that things would definitely "go back to normal." I remembered normal....surely, it was just around the corner, as soon as I got through this little hurdle...or maybe this one...or it's gotta be coming now.... You get the idea.
Your Father is sick. I urge you...if you haven't already, to do some research on what chemo can and does do to a body. It can be shocking just being around it 24/7, but if you aren't, and you see him after a few weeks of being away, you need to be prepared. Prepared enough to potentially be able to keep a warm, loving smile on your face and in your eyes when you see him, if he is doing poorly. Have something positive to talk about--something interesting. You'll run out of things to talk about after you ask him about what is going on, and how he feels. There will be that awkward pause...and you need to remember, no matter how stressed you are, he is infinitely more terrified, even if he never admits it. Don't be afraid to touch him and hold his hand; often people on chemo come to hate the nurses and doctors that are forced to give them that horrible stuff; touches of sincere affection make a great salve to that. You need to be able to explain it calmly to your children, in terms they can understand and that won't frighten them more than they already are. Sadly, I have been through chemo with my Dad, and with previous partners families...these are just a few things I've picked up.
Most important: keep that appointment. And afterwards, do something for yourself--and by yourself. There will be a lot to process. Go see a movie; have an ice cream; go to the mall and count how many teenagers with funny hair. Play GTA and beat the living crap out of everyone you see. Just something completely for you.
Then breathe.