I don't see it as being a gold digger at all. I think she is just telling you what is going on because she feels free to open up to you.
You are her sounding board. Maybe you think she is looking for finacial help because a lot of men(not all) think women want something or some kind of help when they talk about their problems. Usually, we just want someone to listen. I would say just keep listening and perhaps tell her that she could look into getting the child support she needs and you could help her with the paperwork or something. See what she says or does from there.
