I would definitely recommend that the mother does not project her negative feelings for the absent father on the children. If I could have made one change to my life growing up, it would be that I wouldn't want to hear all the horrible things that my mother always had to say about my father.
Other than that, the mother should always make time for her children to listen to what they have to say. Children are intelligent people and they can have some very important things to say.
And finally, I would say that the mother should always love her child, and that she should understand that it's just as hard for a child to have one parent as it is for the mother to raise the child alone.