Thanks for linking to the filing.
The stuff about losing custody is pretty bad, and thanks to Meghan's previous lawsuit, there's no doubt that she said it and intended it for broad publication. The same is true of the claim about Samantha changing her surname to "Markle" only after Meghan began dating Harry. That one, she said on Oprah. I'm singling out those two, which I've commented about previously, because it will be very easy to prove whether or not they're true. Name changes and custody decrees are both legal documents that would be on file with the relevant local court. It shouldn't be too difficult to prove who lived where when, either.
The rest of it may all be petty tit-for-tat, but unless both of the above statements are true, I don't think this case is going to go away quietly. Maybe I'm wrong, and Meghan (or her staff) did all necessary research before making those claims. But I don't think so, because the child custody claim was made in a document she prepared herself and that Knauf advised against sharing with Scobie. And she didn't even research the basic rules for titles before making claims about them on Oprah, so I rather doubt she was calling courthouses and looking up name change documents.