Hey NotAHero;
She continues to blame me for the relationship failing, gas lighting and guilt tripping. I have to communicate with her because we have a child together. I don’t respond to most of the negative comments.
will this go away eventually ? Like when she officially move on? Is there a better way to handle it?
Each situation is different. My DH and his kids' mom divorced ~11 years ago. She still makes passive-aggressive comments to him in texts & emails, and is uncooperative about parenting time. Based on things the kids say, she still blames him for things that happened when they were married -- like, of course she always wanted to be outdoorsy and go hiking, but he wouldn't let her. Um, it's the opposite.
Part of our dynamic is that about 3 months after the divorce, she got engaged to DH's then-best friend, and they were married 3 months after that. DH's (former) best friend and his ex admitted, while DH & ex were married, that they were attracted to each other. Former Best Friend has strong NPD traits and a history of "my dad left so I became the man of the house, and I'm just not the kind of guy who leaves families... but you [DH] are"
So while some pwBPD, after a divorce, "tone it down" in a new relationship, the opposite happened for us. The NPD-BPD dynamic has kept fanning the flames of blame for over a decade. It's not as overt but it's still there and toxic.
To answer your question about if there's a better way to handle it than ignoring the negativity, in brief, no, you're doing well. It's a critical skill to have -- to identify what in the email is actually about kid logistics and what is just disordered filler, and then to have the discipline to only respond to logistics and not take any other bait. If you're already doing that, and steering away from Explaining yourself, Arguing, Justifying your parenting, etc... you're miles ahead of most.
You've probably already heard of BIFF as a communication scaffolding? That's another tool to use: keep any texts/emails Brief, Informative, Friendly, and Firm. I try to keep anything I send to the kids' mom equivalent to a business email in tone, and as short as possible.
Because DH's kids are older than yours (they're 13 & 15), Mom is again trying to send messages through the kids, but really subtlely. I'll send an email asking something, and she won't email back, but one of the kids will tell me later that "Mom said it's fine if I do X". I tell the kids "Great, I'll check my email to see what she says" and I do NOT, repeat do NOT, send a followup email asking "hey, the kids said you said they could do X, let me know any updates". She's a grown woman with a phone and computer. She can figure out coordinating if she chooses to.
...
I hope our situation is uniquely horribly long-lived and that you do not experience that. Also hope this was helpful food for thought...
kells76