There are actually a few different questions hidden here so I'm going to try and address as many as possible in a small space.
1.) Busyness does not equal being under Satan's yoke. If being busy distracts from what God is saying and trying to lead you to do, then it can be a tool the enemy uses to distract. It is unfair to characterize an entire person that way because they missed a family event.
2.) There is nothing wrong with the KJV. As far as I'm concerned, if the truth written in the Bible is communicated to the reader in a way that God can speak clearly to them, then that's what it truly important. I am a huge fan of accuracy to the original text and not big into paraphrases. That being said, everyone reads and understands differently. It is also unfair to judge someone based on the version of the Bible they read.
3.) To the original question, I would direct you to Romans 12:14-21. One of the best ways to handle this situation is essentially what alfetherlin said. By being kind, you will actually directly impact the attitude someone has towards you.
I will add this, however. I don't believe you should be walked over, nor should you allow yourself to be. From the story you tell, you may not be the only person they treat this way. For that, I would direct you to Matthew 18:15-17. Talk to them about their attitude and how it affects you.
Note: This does not have to be, nor should it be an attack on that person. It should simply be an expression of your heart in an attempt to resolve the issue. They may attack you in response, but you do not have to retaliate.
Try to be encouraged that you are not the first, nor the last person to encounter that type of attitude, even from family. You are not the first to miss a family event because of work, nor the last. It is ok.