If you were ever in a room with Richard and Lorelai Gilmore, you wouldn't necessarily think they were related. Well Lorelai Gilmore the second, Richard had an undeniable relationship with the first and third, but there was never a great relationship with his daughter.
No one really knew why, some said the distant generations or that his daughter had simply not been or done what he wanted, and he didn't know how to relate, but none actually knew that the non relationship was their relationship. It was predictable and it was always like that and Richard had no intention of changing that.
He didn't see why it was anything but productive, he knew that Lorelai was unpredictable and things that he hadn't even thought of would happen, seemed to happen to his one and only daughter. She got pregnant at 16, and even though he would have never guessed, he should have expected it. Lorelai always did things in a skewed kind of way. When she was a baby she could run before she could walk, she could say sentences before she uttered single words, Lorelai Victoria Gilmore was an enigma, just like his beloved Trix.
The one thing that Richard adored about his daughter (not that he would ever utter the words to her) was her grin. A breath stealing grin that seemed to illustrate Lorelei's mischief and vivacity for life that seemed to run through her veins. She would flash this smile and he would find himself trying to stop grinning himself in response. She used to flash this grin after she had uttered a truthful but not appropriate remark about dinner or anything to Emily, which would make dinner even tenser.
He never told anyone, but he was more than pleased that his first daughter was like Lorelai. He hadn't expected Lorelai to be their one and only child, but Richard never complained that there wasn't a male to carry on the family name. Family pride is one thing, but he knew how ridiculous it is to not appreciate what he has.
He may scoff at the scandal that Lorelai brought to the family, and her escape to Stars Hallow may have brought more pain to him and Emily, than his daughter will ever know, he is proud of her. To see her stand up for herself time and time again, and raise Rory with such conviction and moral fortitude, it made the name Gilmore stand out.
Simply, his and Lorelai's relationship wasn't conventional, but he loved his daughter, and he would always love her, scandalous behavior or no scandal. Luke, the gruff unshaven diner man or Christopher, the man who had deserted his daughter and granddaughter repeatedly. He was a proud man and he was proud of his daughter.