The only time we see Lord Alan in the book is in the very beginning, when he tells his children that being sent away "is my decision. We need not discuss it" (1.1). So, he's not exactly the ideal image of a caring, involved father. It's not like Thom and Alanna haven't noticed. When Thom observes that their father doesn't care what they want, Alanna answers: "We know that…He doesn't care about anything, except his books and scrolls" (1.3).
Of course, Lord Alan's indifference is hurtful to his children, but it also helps them pull off their ruse. Fair trade? Because of Lord Alan's famous inattentiveness, Alanna is able to convince Lord Gareth that her father actually made a mistake in checking to see how his son "Thom" was doing at knight training, since Lord Alan could never tell his children apart.
There's a reason for Lord Alan's weird behavior. As Alanna says, "My mother died having Thom and me. She had the Gift too. Father was angry—he thought their magics should've saved her. So he said he wouldn't ever use his Gift again, and we weren't to use ours" (4.120). Sure, losing your wife is a pretty raw deal … but that's still no excuse to get your kids mixed up.