Hunter and Kathleen Biden just turned down the volume on their nasty divorce ... according to new legal docs.
Joe Biden's son and daughter-in-law filed docs Wednesday -- obtained by TMZ -- calling for a stay of litigation in their divorce proceedings ... which means they're putting down their swords until they can "amicably and privately" reach a settlement.
It's a complete 180 from last week when we reported that Kathleen filed docs accusing Hunter of blowing all their money on booze, drugs, hookers and gifts for other women. He fired back with docs of his own demanding any proof SHE had cheated.
The new filing makes it clear they're trying to follow the Gwyneth Paltrow-Chris Martin "conscious uncoupling" playbook ... instead of taking the nuclear option.
The judge still has to approve their request, but that's a formality.