Most public defenders are very good lawyers but just like anything else there are some better than others. In addition, even the best public defenders are sometimes over burdened with huge case loads. You either have to make the best of it or somehow find the money to hire a lawyer of your choice. Making the best of it means trying to get the best out your attorney and staying on top of your case without being rude or a pest. Ask to have an appointment to sit down and discuss your concerns. You have very serious charges so don't let time go by without addressing the issues. If for some reason you feel that she just can't handle your case you can ask to speak to her supervisor. However, you have to be very careful that you don't turn everyone against you. Be sincere and reasonable. Almost all public defenders really want to do their best to help you.
Public Defenders, in my opinion, are some of the best trial attorneys there are. Why you feel yours is "scatter-brained" and "lazy" is not clear from you post. If the only evidence as you say is the complainant's statements, I don't know how complex a trial it would be or what you expect your P.D. to be doing that she is not doing. She is ethically obligated to present you with any plea bargains she receives from the State--which she has done--and you have rejected them as is your right.
While the high caseload a P.D. might carry is a concern, private attorneys, again just my opinion, don't find it financially sound to try a lot of cases. A private attorney who knows that a case is going to trial is going to charge a substantially higher fee than s/he would for a case that has guilty plea written all over it. However, not all attorneys will charge the same thing. If you haven't, why don't you shop around and get consultations and quotes from some private attorneys.