Yes, although the court has a presumption that the appointed person is who the deceased want. You have to show more than just you don't like or trust that person. If you are able to have the court appoint someone as executor / personal representative for the estate that will not remove that person as a beneficiary of the will.
I am sorry to hear that you and your family have been through so much. It is possible to contest at Will in the Probate Court, but you must be very careful to follow the correct procedure. Otherwise, you may lose your ability to contest the Will.
All of the heirs at law of the deceased should receive a notice from the Probate Court (called a "Citation"), which provides notice of the Executor's petition to probate the Will, and which provides for a certain date by which all objections to the appointment must be filed.
Your next best step should be to make contact with a lawyer who is experienced in the area of probate and probate litigation.