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I'm with you. I think the question defeats itself.

You were born. What has occurred in the past cannot be changed because I'd imagine principles in the Universe would be self protecting against such anarchy as going back and preventing that what HAS happened, from happening. It's a nonsense, because either it did, or it did not. And it did.

Meaning: there is a huge arrogance in an assumption about going back and killing your grandfather - you can only know so much about the past, and nothing about your future.
In your future, you anticipate going back and making the kill.
You go back to the past and find you'll find that your gun jams, or you miss the train, or you trip and break your ankle and any number of number of literally limitless possibilities that will conspire to maintain the continuity in the Universe or dimension in which you presently reside - the one in which you exist. Your grandfather will survive no matter what you do - he MUST, or you would not exist.
Even while you are programming the co-ordinates into your machine, you should be thinking - "I am going back - therefore I failed. If I could succeed I wouldn't be here to be doing this in the first place".

That's if going "back" is an option anyway, which I don't think it is. Another story, perhaps, but I'd imagine part of the Universe protection against anarchy is that it's not possible and if it were, the only way the scenario can work is in the answer above yours, where you interaction with the past of ANOTHER dimension or reality, not your "own".
As above, the fact of your existence means it's impossible to change what has already been for yourself - you will have killed an "ALTERNATE" grandpa. You get home and yours will still be in your house.

Better to get some counselling and learn to live with each other.

gvvv.