Describe your character’s relationship with their mother or their
father, or both. Was it good? Bad? Were they spoiled rotten,
or ignored? Do they still get along now, or no?
Q is neither parent's favorite child, but that has less to do with him directly and more to do with the timing of his birth. (He's the third child after all; in some schools of thought he is practically superfluous.)
It's no secret between the brothers that Sherlock has always been their mother's boy, bright of eye and indomitable in temperament; Sherlock is the distillation of their mother's fire, the kinetic passion that drove her to the top of her field and then later led her away from it. And Mycroft—calculating, impossibly intelligent and politically savvy—was their father's hope; on his eldest son did Father Holmes lay all his aspirations, rightly judging Mycroft to be ambitious and yet never understanding quite how spectacularly inadequate a descriptor something as simple as ambitious might be in regards to the sort of measured infamy Mycroft cultivated.
Nevertheless, qualifying the variables does not change the sum of them: Mycroft is their father's favorite; Sherlock, their mother's.
But Q is their third living child, their youngest, and despite not being the favorite, he was still undeniably cared for. He wanted for nothing, in material or in support; his mother loved him no more or no less than her other children, and his father struggled with Q's temperament as strongly as he had Sherlock's, though in a different vein. (Still, when Q fled the country, it was his mother to whom he addressed his goodbye letter.) But he loves his parents well enough, and respects them in degrees.
He exchanges emails with them periodically, more often with his mother than his father; it's his method of keeping in touch, and it does the trick. Q considers his current relationship with his parents healthy, though not overly close; he doesn't come home often, except when he can't find an excuse to avoid it.