Sweetie
Beloved
Main Squeeze
Long-Term Partner
SO
Honey
Where the fuck have I said that the woman is a “giant ho ho”, whatever in hell that means? I have no knowledge of or have an opinion on whether she (or he) lives a “chaste” or “licentious” lifestyle frankly I don"t care. My entire point for this thread was as is ponted out above to see how a relationship of this sort can be described. If that offends your sensibilities then by all means ignore this thread, in fact I think everyone will better served if you do just that.
Why are you thinking of calling her?
If you know her name why not avoid the issue entirely and refer to them as “Mr X and Ms. Q” in conversation? Sounds like you are mostly discussing her with other people who know the situation. If I am talking about unmarried couples to others who know them I’ll just use their names.
Otherwise, if speaking about them to someone who only knows one “Mr. X and is significant other” or “Ms. Q and her significant other” is sufficiently descriptive and clear to others without getting into any speculative terms. It is possible they have agreed marriage is not for them for whatever reason but legal provisions have nonetheless been made for her and the children. In addition to whatever their intimate relations are they clearly put each other in traditional marriage roles publicly, so that is how they have chosen to be regarded.
I’m not sure why you need a highly specific term. All that matters is that there is clearly some sort of romantic relationship between them. That they don’t live together, that they may or may not have kids together, why does that matter? If you were to call her his SO or girlfriend or ladyfriend, would someone really be utterly confused by the specifics of the situation?
As for the term I’d use, girlfriend is appropriate. If the age is up there, I suppose ladyfriend does too, but that’s more something I imagine a dad introducing his girlfriend to his kids would say. And if you’re not sure, SO seems to be basically the catch all for precisely this sort of situation that is more serious than a casual dating relationship. But really, since they’re not married or engaged, girlfriend is the appropriate term.
Sure, technically the denotative version of mistress as used 50-100 years ago is a pretty good description, but these days it’s generally insulting. Personally, in that social setting, I’d rather go with less descriptive but uninsulting than more accurate and probably insulting. And, well, concubine, even if it were accurate, is just so outdated and bizarre, it ought to raise eyebrows. When I hear that term, I think of essentially slave women taken as trophies from conquest or at least a polygamous culture. At the very least it implies a negative view, even if none exists.
Most likely, no. Common law does not mean any man and woman in a relationship. It doesn’t even mean any man and woman, having sex, and living together. A true common law marriage is just a marriage that doesn’t have it’s basis in a signed legal contract “marriage license”.
As far as I have ever found, Utah is the only state that doesn’t require that the man and woman consent to being married. In other words, except possibly in Utah, just living together or having sex doesn’t automatically lead to a common-law marriage.
Having lived with my SO for 20 years, I do occasionally check the current status of common law requirement, to make sure that we haven’t ended up inadvertantly married, just because we checked into a hotel in Texas as Mr and Mrs (there have been myths around stating that).
A ho ho is an disgusting and unlamented snack food put out by a bankrupt company. I said “ho.”
Nope. The title of this thread is “what would you call the woman in this relationship” and your suggested terms refer to her. You haven’t answered questions that ask why you need a term to refer to her specifically and not the gentleman in question or the relationship in general. You keep saying that you aren’t making judgements about her sexual life, but you repeatedly refer to her in this thread using loaded terms and have rejected other less judgmental terms for stupid reasons. You haven’t responded to any of the posts offering reasonable alternatives and you still haven’t managed to articulate why any of this is any of your business at all.
I guess you could refer to her as the mother of his bastard children.
Honestly, as Princhester said, the specifics of their social situation are unusual, and English really doesn’t have a single word that describes their exact relationship. Girlfriend is closest, I think.
Vaginal access facilitator.
Word.
Happy. Otherwise she would not be with him. 
Why won’t plain ol’ girlfriend do?