It's about a grandmother who forces her grandchildren to live in her attic and their mother knows they're being mistreated but doesn't say anything because the grandmother spoils her. One of the children has a pet rat and it bites him and he gets rabies and dies. What's the name of the movie?

Except for the pet rat with rabies, I'd think it was this film:

Flowers in the Attic (1987)
Starring Kristy Swanson, Victoria Tenant, Louise Fletcher
IMDb synopsis:
Children are hidden away in the attic by their conspiring mother and grandmother. After the death of her husband, a mother takes her children off to live with their grandparents in a huge, decrepit old mansion. However, the kids are kept hidden in a room just below the attic, visited only by their mother who becomes less and less concerned about them and their failing health, and more concerned about herself and the inheritance she plans to win back from her dying father, to the point of murder.

Flowers in the Attic (1987) - IMDb