Yes. This is permissible. Depending on your estate plan, you may want an independent (non-related, non-subordinate) party to serve as fiduciary (particluarly of any trusts that may be established upon death). You should speak with an estate planning attorney to guide you through the selection of fiduciaries and a coordinated estate plan.
What does the will say? Are there alternate executors named? If not, then a relative may petition the Surrogate's Court. However, the Court will be at liberty to make the appointment to qualified persons absent clear direction from the testator.
Send them a certified letter that they are only to correspond in writing. In the letter, ask them to validate the debt under fair debt collections practices act and have them remove it from your credit within 30 days under the fair credit reporting act if not validated. Have an attorney ready to answer the complaint if they serve you and then have the attorney serve them with a discovery request. (All of this is very technical and I would not recommend you do this yourself). Then have your...
Make sure to hire a lawyer and have that lawyer send a Fair Debt Collections Practices Act notice to the debt collector. You can sue under that statute. Also, check your title insurance to see if you have coverage for this item. If you do, the title company is responsible for defending you and clearing the cloud on title.
Your will and your wife's will are coordinated such that if you were to die in a common catastrophe, there would be a set order of who died first to take advantage of both spouse's estate and gift tax credits and get the step up in tax basis to date of death value for assets. Usually, the husband has more assets in his name, so his assets pass through his estate to get the step-up in basis and fully use the available credit / applicable exemption amount.