How does father get custody?

If the children have been living in Alabama legally for at least six months, the custody case will have to be heard there.  Otherwise, if the children were in the last state before Alabama for at least six months, that's their "home state" until the six months in Alabama are complete.

The case gets started with a petition for custody;  while the form might be slightly different in some states, it isn't really any different than filing a complaint to start any other civil lawsuit.

Ordinarily, when a child's mother dies, the father has the best claim to custody.  That might be a bit complicated here, depending on how long ago mother died and what father has been doing in the meantime.  But the basic principle should still have at least some weight, and if you can prove abuse, the father has a good chance of getting custody here.