This woman was physically attractive.
I encouraged her to keep attending church and said goodbye.

But I thought, Why would a woman in her thirties choose to have a best friend that is a male?

Specifically I want to follow Dr Harley's advice below:

"I understand how you want your children to have a reasonably friendly relationship with their mother. �But under the circumstances, I�d suggest that instead, you create a wall of protection around your children as long as possible because of your wife�s thoroughly uncaring behavior toward them. �Let them know the full truth about her lack of care for them because of her love for another man. �Don�t embellish the story, just give them the facts. �Sooner or later she will probably try to restore her relationship with them through you, perhaps in the hope that she would receive some kind of financial support from you or the state if she were to have partial custody. �But I would let them know that not every mother loves or knows how to care for her children. �Sadly, their mother is probably one of these people. �Plan B is probably the best way to create that wall of protection."

Any thoughts?

Why not? Maybe she is divorced, maybe she is a widow.
Maybe they run a business together or a charity with consent of their spouses.
Maybe they are having an affaire.

The first thing you notice when meeting these ppl is the womans physicals, perfectly normal.
Next you seem to WANT to judge their relationship as either proper or improper, although you have no real evidence to support either theory.
The woman communicates with you that its ok to approach.
Why do you feel the need to assess their relationship further, before having a deeper conversation with them both?

As for the advice of the Dr. Is there a possibility to relocate your family away from their mother?

dr Harley said on the Radio Show that if the person does not attempt suicide then there is no BPD.

After listening to several radio clips, and reading about "Electric Fence" in Buyers Renters Freeloaders book, that describes my ex wife.

dr Harley said on the Radio Show that if the person does not attempt suicide then there is no BPD.

I can't be around people that support adultery like those board members do

Dr Harley also said in a radio call that a BPD would not end a relationship. They cling to it.

Wait.
I don't allow my wife access to my children.
I followed Dr Harley's advice and I have full custody. She has supervised visitation. That is ordered by the court. I dont have control over what the court orders.

He consistently says that personalities cannot be changed.

True, but a bit more nuance is in it's place here.
One of the personality traits of a BPD is;

FEAR OF ABANDONMENT

another one that is NOT described in the DSM IV medical guide as it is only apparent witin a relationship is:

THE PUSH & PULL CYCLE
http://www.downwardspiralintothevortex.com/2012/03/push-me-pull-you-push-pull-cycle.html

Rings a bell?

One of the personality traits of a BPD is;

Borderline Personality Disorder DSM IV Criteria

A pervasive pattern of instability of interpersonal relationships, self-image, and affects, and marked impulsivity beginning by early adulthood and present in a variety of contexts, as indicated by five (or more) of the following:

1. frantic efforts to avoid real or imagined abandonment. Note: Do not include suicidal or self-mutilating behavior covered in Criterion 5.

2. a pattern of unstable and intense interpersonal relationships characterized by alternating between extremes of idealization and devaluation.

3. identity disturbance: markedly and persistently unstable self-image or sense of self.

4. impulsivity in at least two areas that are potentially self-damaging (e.g., spending, sex, substance abuse, reckless driving, binge eating). Note: Do not include suicidal or self-mutilating behavior covered in Criterion 5.

5. recurrent suicidal behavior, gestures, or threats, or self-mutilating behavior

6. affective instability due to a marked reactivity of mood
(e.g., intense episodic dysphoria, irritability, or anxiety usually lasting a few hours and only rarely more than a few days).
7. chronic feelings of emptiness

8. inappropriate, intense anger or difficulty controlling anger (e.g., frequent displays of temper, constant anger, recurrent physical fights)

9. transient, stress-related paranoid ideation or severe dissociative symptoms

The DSM IV goes on to say:

The essential feature of Borderline Personality Disorder is a pervasive pattern of instability of interpersonal relationships, self-image, and affects, and marked impulsivity that begins by early adulthood and is present in a variety of contexts.

Individuals with Borderline Personality Disorder make frantic efforts to avoid real or imagined abandonment (Criterion 1). The perception of impending separation or rejection, or the loss of external structure, can lead to profound changes in self-image, affect, cognition, and behavior. These individuals are very sensitive to environmental circumstances. They experience intense abandonment fears and inappropriate anger even when faced with a realistic time-limited separation or when there are unavoidable changes in plans (e.g. sudden despair in reaction to a clinician�s announcing the end of the hour; panic of fury when someone important to them is just a few minutes late or must cancel an appointment). They may believe that this "abandonment" implies they are "bad." These abandonment fears are related to an intolerance of being alone and a need to have other people with them. Their frantic efforts to avoid abandonment may include impulsive actions such as self-mutilating or suicidal behaviors, which are described separately in Criterion 5.

BPD = Borderline Personality Disorder as desribed by the
Official American Diagnostic and Statistical Manual of Mental Disorders