Per new legal docs, obtained by TMZ, attorneys for the former couple are asking the judge in their federal case out of New York -- which Sophie first filed in September -- to dismiss the entire action ... this in light of the parenting plan they hashed out back in October.

In other words, they're signaling here that they're both on the same page to dismiss this case ... and it all has to do with what they've worked out custody-wise in the UK courts.

While a judge has yet to officially sign off ... this thing is all but gone -- which is a big deal considering how dramatic it was when ST first ran to court citing a child abduction law.

You'll recall ... when she invoked that statute -- claiming, at the time, Joe was preventing their 2 children from traveling to see her across the pond by allegedly withholding their passports -- it elevated that whole matter to a federal level. So, it was on Uncle Sam's radar.

She also claimed they, as a family, had decided England would become their permanent home ... but because Joe was allegedly keeping the kids in NY amid their still-fresh divorce filing, she claimed his actions ran afoul of international child abduction laws.

Since then, of course, she and Joe have landed in a much better place -- yes, their divorce is still proceeding, but they've temporarily worked out who gets the kids and when ... which they're citing here as the reason that this lawsuit she submitted can now go bye-bye.

This just further signals continued efforts by the exes to hash things out privately -- for the sake of their daughters, we assume -- after they kicked off their public split on a particularly bitter foot.

First signs of the pair trying to work things out emerged in October ... they agreed to a temporary child custody arrangement -- with the kids going back & forth between them over holidays such as Thanksgiving, Christmas and in between.

It appears other aspects of the divorce are still being worked out ... but in the meantime, they both seem to have moved on romantically -- Sophie moving on to British aristocrat Peregrine Pearson and Joe to model Stormi Bree.