This!!!
It is obvious that the other couple is in a crisis and Kate is desperate from many points of view…(no doubt, so is Sam) . Sam is likely unaware at this point so anything that would make him catch on is preferably to be avoided.
Like you say, it’s really all in Joe’s hands…and up to Jane to patiently wait for this to play itself out… Still awkward nonetheless…
Kate and Sam’s marriage is not in Joe’s hands, but the way he and Jane allow other people to act around them is. Jane also does not have to wait patiently while someone acts in a way towards her husband that neither she nor her husband thinks is appropriate. She has standing to object and insist that it stop, never mind how the behavior was meant.
Joe and Jane cannot tell Kate what is going on with her or or her marriage. They do not know what her intentions are. They can’t know it and they’d be wise not to let on if they did. It will only make Kate defensive. They also do not need to make connections between behavior they don’t like and other problems Kate may be having in her life.
What Joe and Jane can tell Kate is that they are uncomfortable with the way she interacts with Joe, the way she talks to or about Sam, and so on…whatever. They aren’t the experts on Kate, but they are the experts on themselves and their own boundaries.
“
If your brother sins (against you), go and tell him his fault between you and him alone. If he listens to you, you have won over your brother. If he does not listen, take one or two others along with you, so that ‘every fact may be established on the testimony of two or three witnesses.’ If he refuses to listen to them, tell the church. If he refuses to listen even to the church, then treat him as you would a Gentile or a tax collector.”
Matt 18:15-17
Since Joe is married and since Kate’s behavior is therefore offensive to both him and to Jane, and since Jane has witnessed it, Joe and Jane ought to tell Kate that they find it inappropriate and insist that it stop. If she will have none of that, then they ought to involve Sam–again, specifically avoiding saying that Kate has designs or something in her mind, but that her behavior is making them both uncomfortable and needs to stop. (“What, you think she’s coming on to you?” “I don’t know what she has in her head, I only know that I don’t like it when she does X, and since it is a pattern I want it to stop.” “You think she has a thing for you!” “You aren’t listening to me. I’m not her confessor. I want her to stop doing X, Y, and Z. I’m married, and I don’t allow that from women who want me to consider them friends. That’s really not very difficult to understand.”) If both Kate and Sam refuse to see anything wrong with their behavior and won’t stop it even at the cost of their friendship with Joe and Jane, then Joe and Jane take their bat and ball and go home. It’s not easy, but it is fairly straight-forward.