They will not get it because it is not about them or anything they understand.
Agree with AdventuringAbout when they say.. It is rough on you in all sorts of ways, but you are of course dead right to keep putting your boys' needs first. It is really sad that you're being made to feel conflicted, but there really isn't a justifiable conflict here - you are doing the right thing for your sons, and people who are able to understand and support you are worth their weight in platinum. Take great care of yourself, and go gently..
Tell your parents that they can visit you, by agreement, be clear about whether they can stay or not, only you know how much room you have and whether or not that will work etc. Put the ball in their court.
When you go to visit family in Oz you will be based at your in laws because they are able to provide a stable one place base that you can use and from there others can come and see you etc etc if your in laws are happy with this. The alternative seems clearly that you would need to stay at at least two separate locations, which as you say would not be good for your kids.
My kids (birth dd, 10, and adopted ds, 4) just stayed at my in-laws this weekend for the first time, ds has been with us about 8 months. It is about an hour and a half away by car. He coped very well, but then he has settled in very well and we did not have to fly to another country on another continent!
It's totally up to you but I would not make the fact your in-laws are paying into a factor in your decision when talking to your parents (even if it is) and I would just be clear that you and your dh/dp think this will work best for your visit next year.
I am so sad for you that they have been so cruel and lack understanding for your illness, which sounds like a very serious one. If your father chooses to make this the point at which he does not to contact you I would (in light of their cruelty and lack of understanding about your illness) breath a sad sign and await his choice of contact if and when he chooses to make it.
In my personal opinion I would even write an email/a letter to the affect that although you were very sad about their reaction to your illness, you did not go no contact on them and you are baffled your dad would choose to go no contact on you for putting your children's needs first. But if your father has chosen this that is his choice and when he is ready to make contact again, you and Skype and your dh/dp and lovely kids are all there waiting to be contacted (well I would imagine you would be but maybe not, he is in danger of isolating himself isn't he!)
Then I would leave it. Because life is too short. 
Enjoy your family.