Ok, so let's try to break it down...
You get around 3 nights a month to be alone, or go out, with K.
Do you see him only at these times, or do you have any other time? What's the time like outside of physically seeing each other? For example, my girlfriend and I only see each other every 3-6 months, because we are in separate countries. But we spend 5+ hours a day on Skype. This was a struggle for GF's husband. How much time are you and K investing in each other? Is there anything that springs out at you in terms of a reason why M might resent the relationship?
K's wife, M., has another partner who lives in another country, but he comes to visit once or twice a year and stays with them for 6+ weeks.
I'm curious about why you added this. Do you subconsciously feel that M is being selfish, because *her* boyfriend comes to stay for 6+ weeks - yet she can't spare K for more than 3 nights a month?
If so, poly isn't necessarily about 'fair and equal'. It's about practical, compatible, comfortable and agreed.
Practical - plane tickets cost money; lengthier stays make sense
Compatible - M and boyfriend both want that amount of time
Comfortable - M, K and boyfriend are presumably comfortable with this
Agree - that's their arrangement
You and K:
Practical - after kids, work, etc, how much time do you have?
Compatible - what do you both want?
Comfortable - what are you, K and M comfortable with?
Agree - what are your written guidelines? don't have any?
Recently, there have been a couple of incidents where it really feels like M. resents K's relationship with me. (Even though she was the one who suggested the two of us start dating in the first place.)
I hear this a lot in poly. Sometimes people suggest their partner dating for selfish reasons (yay! I'll get more alone / own dating time). Sometimes it's because they feel more in control; thus, less jealous, of the situation by orchestrating it.
Surely she didn't suggest you date, viewing you as platonic friends... then BAM - you became attracted overnight? Surely you two were attracted before she suggested it.... and perhaps that's why she suggested it?
Just because someone suggests that two people date, it doesn't give those two people carte blanche and it doesn't mean that the person suggesting it will feel 100% at ease!
However, I'm not saying you, or K, did anything wrong here.
Do you have guidelines? Written or verbal? One of our written guidelines is that we don't text or call during dates, unless it's an emergency. We don't set a limit on the amount of times we can see other partners - but we have a general verbal agreement that once a week for up to eight or nine hours is on the higher end.
Do I just let it go? Do I tell him how upset I really am?
I think that you all need to talk and re-work an agreement. You don't even have to express upset or annoyance if you don't want the conflict. You could word it as "would you mind if we can set some expectations regarding time with K? I don't want to interrupt you two when you're spending quality time and I think it would help me to know what to expect."
Or is this just karma coming back to bite me? A few weeks ago I did something inconsiderate that really hurt and frustrated my husband and I felt awful about it. I did everything I could to make it up to him, but maybe karma just needed to give me a good bitch-slap about it, just to be sure?
Karma is a bitch, for sure! But, Karma or not, I don't think it's acceptable for K to leave halfway through your time to go to a bar with M... nor for M to request it.