Nearly all cases are settled by plea bargain. But, trial or plea bargain is your choice. Simply "wanting" you to take a plea is not misconduct, it is advice which you should consider carefully. HOWEVER, you can replace your public defender with your own attorney at any time. Simply retain your attorney and your new attorney will notifiy the court, prosecutor, and prior attorney of the replacement.
Let us know how the works out for you.
We do not have a client/attorney relationship until you make an appointment, we discuss your case face to face, I accept a retainer, and we explictly agree to enter into representation.
You can tell your attorney that you want to fire him or her. You can tell the court that you want to fire your attorney. You will have to give reasons, and his or her wanting you to take a plea offer is not going to be good enough because it's their job to give you advice and if they think that's a good option for you, they have to tell you that. If you want to go to trial and don't have confidence in your attorney's ability to try the case, tell the court and your attorney that and give reasons why this is so.
As the other attorneys said, you can hire your own attorney at any time (although the court may not allow it if your case is very old and a new attorney would mean continuing your case).
If you want a different court-appointed attorney, that is more difficult. You can let your attorney know and they can note a motion so that you can address the court. But, not liking your attorney or their advice is not going to be enough to get you a new attorney. You will need to show that communication has broke down and you are not able to work together or some type of misconduct.