I'm going to post an answer that relates to things I need to personally do for my Dad and may not be completely relevant to your situation, but may contain some useful ideas and be helpful for someone else. Unfortunately, it's super hard to predict how someone is going to act without knowing them personally.
When I was young, my Dad was not very good at dealing with the frustrations that I apparently laid upon him and to this day, I am sure that I irritate him. That said, I am a grown adult and do not care for a lot of his methods of controlling a situation, which have included physical and emotional trauma that I will not tolerate ever again from him.
He has since gotten better, but I don't think it's he himself that has gotten better, but rather his fear of the social repercussions and how he will be perceived in society by his peers that keeps him in check. When I talk about physical trauma, he was at risk of being jailed at one point for those actions and notably changed his behavior as a result, though, I'm sure much of this change is a repression of his true nature.
From what I know of my father, the most important thing to him is that he's perceived positively by others. This means, he will do any and all of the following regularly:
- He doesn't outright lie, but tends to lie a lot by omission to ensure he is perceived well. He also gets apprehensive when I reveal a truth about him. A lot of times his lies are casual and kind of funny, but he has had people genuinely think his career was chef for a weirdly long time. But this extends to me not really knowing or understanding what his job was until I was 26.
- He believes he is a better parent than his father. I suspect this is true. From what family lore I have been able to gather (we've a lot of secrets), my grandfather was a miserable, abusive parent, and his death was a good thing.
- He tends to think that any help provided is useful and takes personal offense to being corrected on this. For example, we moved across the country and he told us to not bring our kitchen things because he had everything we could ever want. Apparently, everything we could ever want was utensils, 3 glasses, a sauce pan, and a blender with no blades. The blender with no blades has become our description for my Dad since then.
Prior to my daughter being born, I attempted to talk to him about this in a public setting since it's the only location where I feel I can count on him to not lash out excessively. As best I can tell, he more or less shut down.
Now that my daughter is here, I am going to have to talk to him again. And it's going to have to do with his lying. Working up the nerve is the hard part. I am considering having my wife present so that we can approach this together, but that is the sort of thing that's likely to make him apprehensive because he has a social face and a private face and never wants the two to mix.
I recommend the following steps for this conversation:
When you are worried about how someone's going to react, I find it's best to do things publicly so there are social mores forcing them to control themselves to an extent. It will make them listen to you carefully, mull things, and respond carefully. Either going out to eat, a walk in the park, or something else. You should pick a place they are comfortable in, though.
This is a family matter and needs to remain as such. My Dad's response and handling of a situation will be very different if he has one of his friends around. In addition, this is very awkward for that friend. Do not handle this conversation in front of your parents' friends. It can be handled in front of your friends contingent that they understand their presence is to support you as you deal with this. This permits your parents a means to save face publicly.
Write it Out
I got emotional last time I tried to address this with my Dad and forgot half the things I wanted to bring up. I think it's helpful to have a written list of events that illustrate the point you're trying to make since oftentimes it's not a singular instance that's the problem, but the overall pattern.
This issues has risen to a peak that needs to be addressed. It will help if your written information includes what you need from them. It sounds like you want to be able to live with your significant other without them trying to slam you for not complying with 'tradition'. As someone with nothing to lose giving solicited advice, I would state clearly and plainly that they are going to need to let go of tradition and stop bringing it up. And this would include when you're not there since it's going to affect their body language if they're complaining about it behind your back when you aren't there.
I can't stress enough that whatever measures you are willing to enact in response to this can't be idle threats. If they are, you will find your parents are willing to toe the line and if you say nothing, they will see how far they can go. That said, failing to meet your requirements perfectly probably also shouldn't be grounds to cut them off. I try to set the expectation that I want to see continuous improvement. And if they don't seem interested in that, you should be willing to enact whichever measures you indicate being willing to do.
Personally, I cannot guarantee that this will work for you. I can say that it will be grueling and I'm not looking forward to doing this again with my Dad. With my Dad, I have found that he knows of my irritations and now every event with him always includes at least 3 or 4 other friends of his. It's likely his way of keeping himself in check, but he still says some casually insulting things that I don't call him on often enough.