a bit about Albert and his dad: Although we don't see Albert's drunk father at the end of the book, Albert tells us a little bit about him: he's always regretting selling Joey; he's quit drinking; and it turns out he's kind of a nice guy. Albert seems to have forgiven him, proving that horses aren't the only ones capable of forgiveness.
a bit about Albert's mother: We don't see Albert's mom too much. She basically spends all her brief on-page time trying to convince Albert that his father isn't a terrible human being. We'd love to see the spin she put on the whole selling-Joey thing, but we never see it because the narrative follows Joey away from the Narracott farm and to the front lines of war.
Albert seems to really love his mom, though, and he always does what she asks of him. And after all, she's the one who convinces Albert's dad not to shoot Joey after Joey kicks him. Her heart's in the right place, and she's just doing what she can to keep her family happy and together.
(Hope this helps, great movie & book btw, made me cry the whole way through ToT)