I actually thought that the granddaughter's wording was great. She didn't soft-pedal by pretending that she was the one with the problem, which "It bothers me to hear those words," etc. can sound like. But she also didn't insult her grandfather by saying, "If you use these words you're a horrible person." Instead, she informed him of how the language he chooses makes him sound, especially to people who may not know him well.
Her mistake, in my opinion, was in saying what she did in public. It would have been a real service to her grandfather to get it across to him that his language is widely considered unacceptable today--what is and isn't acceptable changes over time, and not everyone is good at keeping track. Instead, she called him out in front of his family, and so the odds that he would hear and internalize her advice plummeted. He probably felt, in fact, like she was trying to incite the family to gang up on him, and I don't blame him one bit for throwing her out.
I'll give her part score--it's a shame she didn't put as much thought into when she spoke up as into how.