If a lawyer . . . provides legal advice to family member, advocating
they take a child out of state, without filing an order of protection,
an emergency order, petition states the defendant's belief that the
child was at risk if left with the other parent, then are they
potentiality for engaging in custodial interference?
No. The lawyer is not potentially engaging in the crime of engaging in custodial interference.
Note that this is true whether or not the conduct of the person receiving the advice constitutes custodial interference or not.
It is also true whether or not the advice given accurately described the law (unless the lawyer intentionally lied to the client about what the the client's legal obligations were, rather than simply being mistaken, which is a fact pattern not contemplated by the question that would suggest some crime other than custodial interference, solicitation of custodial interference, or conspiracy to commit custodial interference).
Can a lawyer be charged with Custodial interference pursuant to ARS
Obviously, the lawyer providing advice could be wrongfully charged with that crime by a prosecutor.
But if the prosecutor did so, and if the judge then correctly applied the law, then the judge would dismiss he charges, probably prior to trial, because the charges brought were not supported by the applicable law.
In The Case Of A Lawyer
The crime is defined by Arizona Revised Statutes § 13-1302(A), and if that crime is not established, then you never get to the definitions, defenses and punishments found in the rest of the statute. It states (emphasis added):
A. A person commits custodial interference if, knowing or having
reason to know that the person has no legal right to do so, the person
does one of the following:
Takes, entices or keeps from lawful custody any child, or any person who is incompetent, and who is entrusted by authority of law to
the custody of another person or institution.
Before the entry of a court order determining custodial rights, takes, entices or withholds any child from the other parent denying that parent access to any child.
If the person is one of two persons who have joint legal custody of a child, takes, entices or withholds from physical custody the
child from the other custodian.
At the expiration of access rights outside this state, intentionally fails or refuses to return or impedes the return of a child to the lawful custodian.
As the question acknowledges, A(3) and A(4) don't apply to a lawyer providing advice because the lawyer does not have joint custody and the lawyer does not have access rights to the child.
The lawyer has not taken a child, or enticed a child, or kept a child, or withheld custody of a child.
The advice isn't what interfered with custody, it is the act taken on the basis of that advice that causes interference with custody (assuming for sake of argument that it did cause interference with custody).
In any plausible lawyer-client relationship, the lawyer tells the client about the law and what the client's options are, rather than having the power to direct the client to do something for the lawyer's own purposes, so it also does not constitute the inchoate crime of "solicitation of custodial interference".
The hardest question would be whether the lawyer committed the inchoate crime of "conspiracy to commit custodial interference". And, while legal advice would ordinarily be subject to attorney-client privilege, it would still be conceivably possible to prove conspiracy to commit custodial interference if that was a crime, because the attorney-client privilege could be unilaterally waived by the client (it does not belong to the lawyer) or because there is an exception to the attorney-client privilege when the services of a lawyer are used to actually carry out a crime (as opposed to being used to determine if proposed conduct is a crime, or what the lawyer would recommend that the client do).
But conspiracy liability has an intent requirement. You can't negligently conspire to commit a crime. So, a lawyer who provides inaccurate advice that the lawyer believes to be true (committing professional malpractice in the process, but doing so negligently and in good faith, rather than intentionally) does not constitute the crime of conspiracy.
A lawyer who provides accurate advice actually causes the client to face more clear liability for custodial interference because "knowing or having reason to know that the person has no legal right to do so" is an element of the crime of custodial interference, to the extent that the scenario of a lawyer providing accurate advice that the action is unlawful and the client then acting unlawfully is basically contemplated by the statute as the normal case in which the crime arises (for the client and not the lawyer).
If the lawyer provides legally accurate advice, any recommendation about what to do based upon that advice (including advice that it is in the client's best interest to ignore the law because the risks and consequences considering not just the elements of the crime in (A) but the definitions, potential exceptions and practices of the local prosecutor's office, are not as serious as the benefits of doing so) is just that, advice offering the client a chance to make a decision, not a decision itself.
The final decision is up to the client in any genuine attorney-client relationship (as opposed, for example, to an extortionate mob boss-victim relationship in which the boss has ulterior motives of his or her own for asking that this be done, and just happens to also be a lawyer).
Therefore, the lawyer has not committed the crime of custodial interference, or the related inchoate crimes of solicitation of custodial interference or conspiracy to commit custodial interference.
By way of analogy, if a lawyer tells you that it is a crime to beat the man your wife had an affair with over the head with a tire iron, but in your shoes, that is what he'd do anyway, the lawyer has not committed a crime. This is true even if, after receiving that advice, the client, knowing that it is unlawful to do so, goes out and beats that man over the head with a tire iron.
There are a handful of rare cases in the law (some of which have been declared unconstitutional, and some of which have not) in which the act of advising someone that it is in their best interests to violate the law, or encouraging someone to violate the law, is itself a crime (e.g. advising someone to transfer their assets to qualify for Medicaid, or encouraging a group of people to commence a riot). But the crime of custodial interference in Arizona is not one of these rare cases where advice or encouragement is itself criminalized.
In The Case Of Non-Lawyer Advice
In the case of a non-lawyer providing the same advice, it is harder to provide a clear answer, because so many possible fact patterns are potentially involved.
In general, the same analysis applies to advice from a non-lawyer, so custodial interference and conspiracy to commit custodial interference has not been committed if advice is the only thing that has been provided, as opposed, for example, to also providing a car or bus ticket to the family member interfering with custody to help facilitate the transportation of the child.
But the analysis of related offense of solicitation of custodial interference in the context of "advice" from a non-lawyer family member is harder to evaluate.
This is because in a family context, there is a well established line of cases that state that sometimes words that on their face constitute mere advice or a mere suggestion may, in context, actually amount to a non-optional order or direction to take some action, in which case an implied order or request to engage in custodial interference could constitute inchoate offense of solicitation of custodial interference. An order or request, that as a matter of etiquette and civility, is phrased as advice or a suggestion, can still be an order or request that can still legally constitute the crime of solicitation of a crime.
However, if the communication is limited to genuine advice or a genuine suggestion, rather than an implied order or request, then the non-lawyer would not have committed the inchoate crime of solicitation of custodial interference for that advice, for the same reason as for an attorney.
Questions Not Addressed
Note also that this answer does not address two other related questions, which were not asked.
First, would a lawyer have civil liability to anyone to for committing professional malpractice in this situation?
Spoiler alert: The lawyer might or might not have civil liability to the client for professional malpractice, but the lawyer wouldn't have civil liability to a third-party non-client.
Second, would a lawyer have violated any rules of professional conduct that could cause the lawyer's license to be suspended from the practice of law, disbarred, for example, in a manner that does not constitute a crime?
This could be a close call that wouldn't necessarily have the same answer in every U.S. state and would depend upon the details of Arizona law related to the professional ethical obligations of lawyers.
Both of those questions are harder to answer fully, and would probably require a more detailed factual context to answer accurately about what precisely happened in the lawyer-client interaction.