Even though Wart and Kay fight like any typical pair of young brothers, Kay is honestly happy that Wart returns safely from his night out in the forest. See? Kay cares!
But inside himself [Sir Ector] was proud of the Wart for staying out after a hawk, and prouder still to see that he had got it. (S.4.10)
Ector is understandably proud that Wart wasn't afraid to stay out all night in the forest to keep an eye on the hawk. Kay, on the other hand, high-tailed it back to the castle.
He saw that his dear guardian was looking quite old and powerless, and that he was kneeling down with difficulty on a gouty knee.
"Sir," said Sir Ector, without looking up, although he was speaking to his own boy.
"Please do not do this, father," said the Wart, kneeling down also. "Let me help you up, Sir Ector, because you are making me unhappy."
"Nay, nay, my lord," said Sir Ector, with some very feeble old tears. "I was never your father nor of your blood, but I wote well ye are of an higher blood than I wend ye were."
"Plenty of people have told me you are not my father," said the Wart, "but it does not matter a bit." (S.23.65-69)
This is one of the most touching moments in the book, and gives a sense of the family ties between Wart and Ector (and Kay, for that matter). Wart really gets at the idea that blood isn't necessary to make a family. Even though he's now King, Wart can't stand to see his old father kneeling down in the dirt to him.
That is why we have to take note of the parentage of Arthur's son, Mordred, and to remember, when the time comes, that the king had slept with his own sister. (Q.14.19)
The central tragedy of the Arthurian story comes from not recognizing one's own family, which leads to inappropriate and sinful relationships. White is so fixated on this issue that he even presents Arthur's family tree to us. A picture's worth a thousand words, as they say, and this also points to the complicated interrelationships between the historical English and French nobility, which also caused lots of problems.
Indeed they did love her. Perhaps we all give the best of our hearts uncritically—to those who hardly think about is in return. (Q.1.70)
Some people just aren't that into you—even your own family members. And when it's your own mother, it can be especially heartbreaking.
It was strange because it was circumscribed, because it was concentrated on a single intention. They might have been a solar system of their own, with nothing else in space, as they went round and round among the dunes and coarse grass of the estuary. Probably the plants have few ideas in their heads, either. (Q.5.58)
The G-kids are so clannish (how clannish are they?) that they are a solar system unto themselves. Everything else is just empty space—and means about as much to these kids.
I was telling you how [Pellinore] killed King Lot one day, when they were having a practice. It has created a great deal of ill-feeling. The Orkney children have sworn to revenge their father's death, and they are out on the warpath for poor Pellinore's blood. (K.4.36)
All Hatfield-McCoy feuds have to start somewhere, and the Pellinore-Orkney feud starts with a simple accident. Pellinore did not mean to kill Lot, but the bloody vengeance doesn't stop until his son, Algovale, listens to Arthur at the end of the Grail Quest, and refuses to carry on the quarrel any longer.
"He was a brute," said the lady.
"Whatever he was, he was fond of his brother." (K.7.145-146)
Lancelot here recognizes that even brutes need brotherly love. Although Sir Turquine is flat-out crazy, he loves his brother (Sir Carados) enough to want to risk his life avenging his death.
Under the grotesque, magnificent shell with a face like Quasimodo's, there was shame and self-loathing which had been planted there when he was tiny, by something which it is now too late to trace. It is so fatally easy to make young children believe that they are horrible. (K.10.15)
Who planted this notion in Lancelot's noggin? We never find out, but it's hinted that it was someone in his family. This level of self-loathing requires lots of time to cultivate, so it was probably a family member or very close friend. Who might be some prime candidates?
"Blood is thicker than water." (C.10.26)
Yes. Yes it is, Mordred. And in the end, no matter that Arthur's knights once considered themselves brothers, it all shakes down along family lines. It's the Pendragons/Orkneys versus the Dulacs, and it's all for vengeance.