Donnie Jr. posted a pic with his 3-year-old daughter, Chloe, Thursday night ... not long after Vanessa Trump filed for divorce in the Manhattan courts. Don Jr. captioned it, "No matter what is going on bedtime cuddling with the smurf puts a Yuge smile on my face." He ended the post with #bedtime #daddysgirl #cuddle.

As we reported ... sources connected to the family tell TMZ the divorce had been a long time coming. Among the issues ... Vanessa hates politics and we're told the last straw was when someone sent her fam an envelope containing white powder.

One source said Donald Jr. was "relieved."