“What kind of lawyer advises a family to ignore a signed legal will in favor of one that is not signed? “
One knowledgeable in the law?
Certainly not. Probate and wills are a specialized practice. Not every lawyer is well versed in them. You would not consult a malpractice attorney about a house closing. The fact the attorney of record gave the advice he did is proof he is not the one to handle the matter. For one thing an executor does not get to do just whatever they feel like unless such is specified in the will. There is such a thing as fiduciary duty and there is big trouble in store for a person charged with that who just ignores it.
Going by the unsigned will when a signed legal will is in existence(in some states even a halograph will is not considered a legal document)would likely result in a long and expensive legal battle. Maybe even very long and very expensive.