The executor of a will is bound by law to perform certain duties and to act in the interest of the deceased's wishes. The courts will remove an executor on the grounds of disqualification, incapability or unsuitability. Each of these terms is specific and has its own measures. Unsuitability is the toughest to prove, since its measure is the most subjective.
File a complaint with the local probate court to have the executor removed. Which court (county, city etc.) will depend on local codes, although it's usually at the county level. Your lawyer can help you determine that.
Make a game plan as to how you're going to argue this in front of a judge, so you can begin acquiring evidence. A physical or mental handicap is required for a ruling of incapability. A criminal conviction is required for disqualification. If neither of these relatively straightforward assessments applies, proceed to the next step.
Build up a case of the executor's unsuitability, with an eye for ways in which the executor's judgment or actions would genuinely damage the estate.
Find a conflict of interest, if you can. For example, if the executor must sell off stock from the estate in a company in which the executor also holds stock, that would be a conflict of interest. Still, the deceased may have known of it already, which would weaken your case. Also, courts likely won't remove the executor unless he or she sells the stock at a price demonstrably to the detriment of the estate.
Accumulate evidence of misconduct. Examples that could threaten the estate are habitual drunkenness, failure to obey a court order and theft from the estate. Visiting the estate periodically will help establish what has been missing. This step may be necessary for items that are not specifically mentioned in the will but are instead mentioned under a broad heading, such as "jewellery."
Learn what statutory duties the executor may not have fulfilled. For example, the law may mandate filings and accountings that the executor hasn't kept up. If nothing seems like a strong case so far, proceed to the next step, which is the most subjective charge of an executor and therefore the toughest to prove.
Build a case of waste or mismanagement of the estate against the executor. These can constitute both action and inaction, so be thorough and consider examples of both.
There need not be unanimity among the heirs in getting an executor removed. The judge decides if the executor is to be removed, not the heirs.