Don't beat yourself up over this interaction just try to learn from it. Reading your post today was like reading a script for arguments H and I have had in the past.
Just try not to let him push your buttons like that. I feel as if when you asked them something and they don't answer, it means one of two things, 1. They don't know why, or 2. they feel guilty as heck about it and don't want to talk about it.
My H use to say the same thing when we argued about not getting a word in edgewise and he was right, I talk fast and have a habit of not waiting for an answer before beginning again. Silences make me uncomfortable, so I try to fill them in. I am so afraid I won't get to say what I want to say (from being in a big noisy family growing up) that I just talk as fast as I can.
Just breathe!! Evaluate the conversation and file it under a situation you don't want to happen again. I know that none of this is easy. So think about what you could have done better during this interaction. One thing working in our favor is that their MLC brain doesn't retain things long so much is forgotten.
Everything happens for a reason, maybe Dad needs to find that it isn't better out there, he needs to realize how good he had it here. Maybe he will find God and that is the most important thing when he finds Him he will know he is supposed to come home.