My (33/M) wife (33/F) and my parents (early 60's M/F) don't get along, and playing the middle man is pushing me to the breaking point.

I apologize if this is coming off as a bit long winded, but I'm at a big crossroads with this issue between my wife and my parents.
For basically the entirety of our time together (5 years married, 9 years together) my wife has disliked my parents. My wife is very sensitive, and can take things very personally/blow things out of proportion. My parents, who are definitely not without blame in this, can be a bit hard to deal with. My Mom is, to be honest, a bit of a narcissist. She's the kind of person that just isn't super warm, and can say things without a filter, and kind of makes things all about herself. To be honest, it's something I've been aware of, but until I met my wife, I never realized what a problem it was. I think that over time, I've just kind of dealt with it, and just wrote off her behavior as "that's just Mom being Mom," but with my wife being so sensitive, I've gotten better at calling my Mom out on her behavior, though I admit I don't do it as much as I should.
Some other important facts that will be relevant later on: My wife and I live about seven hours away from my parents. I have two brothers, both of them live four hours from our parents (but in different cities). My wife's parents live about 20 minutes away from us, and we see them often.
My wife has high anxiety around seeing my parents. Honestly, it's mostly my Mom; she and my wife are just like oil and water, as I kind of touched on earlier. Part of the reason is that my Mom has a history of saying some unkind things to her, and I admittedly wasn't great about standing up for her. It's something that I've gotten better at, but there's still some anxiety on my wife's part. I'd bring up the topic of my parents visiting/us visiting them once every 3-4 month or so, and usually it would start a big fight. I'd say about half of the time, my wife would agree to see them. We kind of came to an agreement when my wife said she only wanted to see them "a few" times a year. I agreed, mostly for the sake of keeping the peace, but we'd still get into arguments when I brought up seeing them. My wife and I have talked about putting up boundaries with my parents, which I'm working on, and I think I'm doing an okay job.
Our daughter was born two and-a-half years ago. I had always assumed (perhaps hopefully) that my parents would change their ways when they became Grandparents; I had great relationships with my Grandparents on both sides, and was hoping that our daughter would have the same with my parents.
However, it hasn't been quite like that. While they haven't been unkind, they're not the kind of grandparents I was hoping they'd be. For example, they rarely ask about our daughter unprompted. When we FaceTime them, they'll talk with our daughter for a few minutes, then go offI to talk about their own thing. It always feels like they want to be grandparents, but on terms that work for them. I also think it hasn't helped that my wifes parents, who see our daughter often, are the complete polar opposite of my parents; they're your typical lovey dovey grandparents.
In the first year of our daughters life, my wife had a tough time with PPD. As such, I didn't really push the topic of my parents visiting with her or them. Fortunately, due to Covid, I was able to kind of push off their requests to visit us.
Once Covid kind of let up in the Spring of 2021, they came down to visit us a few times. It was okay. My parents didn't really interact with out daughter like we hoped; they played with her a little, but they just seemed interested in working on their laptops and playing on their phones. My wife and I were both upset as to how that trip went. A few weeks after that, we went to visit them at their house, but we had to leave early because our daughter got sick. When we left, my parents seemed upset with us, and kept saying "oh, she's not sick, she can stay, she seems fine," which bothered my wife and I.
Things then were okay for a few months. We saw my parents a few times, but it was mostly at big events (Weddings, Anniversary Parties) so they didn't have much 1:1 interaction with our daughter. The last time they saw our daughter in person was for her birthday party. It felt like my parents didn't spend as much time with our daughter as they did with our niece (their other granddaughter). While I was a little hurt by it, but didn't say anything to them to keep the peace, my wife was completely disraught.
Since then, things between my parents and my wife haven't been great. They've been acting the same; they'll ask about her intermittently, and do the same thing when we're on FaceTime. They've asked me a few times about coming down to visit, but when I bring it up to my wife, her response is "no, I don't think they've earned the right to visit." My wife is of the mind that having a relationship with your grandkids is something that's earned, not given. While I agree to an extent, and I don't think that my parents have earned a free pass on everything, I do think that we could stand to foster a bit more of a relationship with them, but my wife won't have it.
Things have come to a head when my parents have been trying to plan a week long vacation with us, my brothers and their spouses. For some context, my wife and I go to the beach for a week with her family, as do my brothers with their respective in-laws. My parents wanted to also book a vacation house with us, partly because they want to spend time with us, but also, because I think they're jealous.
When I brought it up with my wife, it started a minor fight we ended up compromising that we wouldn't go for the whole week because she didn't want to spend that much time around my parents, rather, we'd just go for four days. I was worried about the optics of how that would look to my parents, but fortunately, neither of my brothers and their families could come for the whole week, either.
I texted my parents to let them know that we'd only be going for four days, and **** totally hit the fan. I received a text from my Mom saying how sad and frustrated they are at how they haven't built the relationship with our daughter that they want to, and that they were hoping to spend the entire week with her. She also added that they keep wanting to come to see us, but I keep pushing them away. My mom then went on to say how she never had a relationship with her Grandmother (my Mom is an immigrant, so she never met her grandmother, as she came from her country of orgin), and that she would be sick if our daughter had the same relationship. She then went on to say how all three of her sons had great relationships with our grandparents, and we (my parents) never stood in the way of those relationships.
Anyways, I'm just at my wits end with this. I can't exactly say "well Mom, a big reason why I keep dodging your visits is because my wife hates you and your visits cause her massive anxiety." I feel like I've been able to put up this charade to them that everything is fine, but this feels like a house of cards that's about to fall over. Honestly, I just want everyone to get along, and I hate that both my Mom, and my Wife are upset at me, but both sides just keep digging their heels further into the ground, and I have no idea what to do here to keep the peace.
TL;DR: My wife and my parents don't get along. My parents want to come to visit us and build a relationship with our daughter. My wife feels that they haven't earned the right to do so, but my parents don't like that I keep denying their visits, but I can't tell them why my wife doesn't want them visiting.


Source.