If my daughter is facing severe child abuse charges and her lawyer is free and incompetent, how doesshe go about having him replaced?

I will assume that by "free" you mean that she has court appointed counsel.  At any rate, the answer to your question is "Yes".  A defendant can request substitution of a PD or the like but a court does not have to allow it.  There will need to be a hearing on this matter.  That means that she can get a different lawyer to represent her if she can convince the judge that it is necessary in order to adequately present her case. 

To seek a hearing for substitution of counsel, she should write a letter to the judge, requesting a meeting with them.  A copy should be sent to both the attorney that she wants removed as well as the prosecutor.  Make sure both copies and the original (which goes to the judge) are sent certified mail, return receipt requested (RRR). She will also need to keep a copy for herself.  This letter should state that she wants her present attorney removed from the case and why.  She needs to list all problems that she is having with her attorney.  The letter should be kept short and to the point.  Be sure that it is truthful, she does not want to jeopardize her position before the judge by stretching the truth.

Additionally, you can contact legal aid and see if they would take you case; if not, ask if they know of an attorney that will volunteer to do it "pro bono" (for free).