If I were you I would just apply for the visa, state that she has full parental responsibility for her son, that the childs father does not support him in any way, hasn't been in contact since shortly after the child was born and that his whereabouts are uknown.
If you actually get in touch with the father or his family and tell him or them of your intentions, it's likely to cost a packet, so if it's at all possible, just keep very quiet about your plans, apply for the visa and see how it goes.