Oh, hell, yeah this reminds me of my last meta. Every single bloody time my partner and I had a date planned he would come over sullen and moody as every single bloody time meta would pick a fight right beforehand. It drove me insane, it was part of a larger-scale pattern in which meta would try to limit my relationship with my ex, which ex was not really okay with and I definitely wasn't okay with.
It definitely sounds like they are working through some stuff, and it's fine and understandable that you don't like what it's doing to your partner and want to do something to help. You can't. You can't because it's not your relationship to fix, it's not your relationship at all. So, where does that leave you? Your relationships- the one with meta and the one with your partner- are compromised and leaving you unhappy. If it's absolutely untenable then it's time for a very frank conversation on how something needs to change. I found my ex wasn't putting up good boundaries with his partner, for starters, he wasn't telling her that he wasn't okay for her to be making demands like she was of him... he wasn't protecting our relationship, if that makes sense, she was making him miserable and he was letting her make our relationship suck as a result. He would break up with her and get back together again and again, at a certain point I jumped ship as I was sick of the merry-go-round. Ex-meta was also not a great communicator, clearly she was not okay with him seeing me and yet as far as I know she never owned up to it, not once. She didn't communicate her needs and fears to her partner, she didn't work through her insecurities, and frankly that's not something anyone can make a person do, they really need to be motivated to understand the crucial need for honesty and intimate communication. Ex-meta and I never butted heads, but we weren't friends to being with (despite my efforts) and certainly we aren't after all that.
Basically, in saying all that I'll add this: what is the practical problem? If they're working through it, it'll get better one way or another, but if they aren't then you will find yourself dragged into a painful, complicated situation. So, if the practical problem is you're in a situation that needs fixing for your own well-being, ask for it. If not, let the figure it out on their own. Don't take it personally, it isn't about you, or hopefully it isn't, it sounds like your partner and your meta are the ones with the issues here, so let them figure it out between the two of them.