Can one executor do things behind the others backs?

No. An executor cannot do anything related to the estate "behind anyone's back". An executor is a court appointed fiduciary who is required by that office to act in good faith. He/she cannot take advantage of that position or cause anyone to unfairly profit from financial transactions from the estate. He/she must follow the will to the letter and make distribution accordingly. Any actions taken by the exeutor should be reflected in the estate file and should be reported in the inventory of the estate and subsequent final account. When co-executors are appointed both should join in every transaction unless otherwise specified in the appointment. If the executor violates the powers bestowed by the court you can petition to have them removed and charged for any damages to the estate caused by their misbehavior. Once the estate has been filed for probate the file becomes a public record that can be reviewed by you at any time. If you think the executor has been dishonest you should report your suspicions to the attorney who is handling the estate immediately. If your complaint is not handled promptly then complain to the court.