I'm glad to hear that you're feeling a little more positive now - a close friend of mine is going through the same thing with his father and he's having to fit in work, trips from here to Bristol to spend time with his Dad and then all the normal everyday stuff too.
So, when he's here I try and drag him out on the bikes, even if only for a couple of hours - he always says that although he didn't really feel like bothering, in retrospect he's always glad that he did.
There's only so much stress, pain and heartache that the human body can tolerate and so we have to have some sort of release for it all, which is what you've found out.
If you were around these parts I'd certainly be there to offer help in whatever way I could, just as with my friend - however, judging by all this training I'd be getting a beasting on the bike rides
All my very best wishes to you, your Dad and all your family - never think that you're alone, that nobody cares and that you have to deal with everything all of the time. Plenty of people care, we've all been there in one way or another.