Shaw's father wanted no monument except the ditch,
Colonel Shaw's dad didn't want him to have a monument honoring his achievement in the Civil War.
Shaw's father felt he should have a more humble (to grossly underestimate) grave—a ditch—and not get special recognition.
It's a little harsh, we think, but it's all about being humble. Biography note: Shaw's father was the first to plant the seed in his son's mind about leading the all-black infantry (which Shaw originally refused). So Shaw's dad thought he was just doing his duty, and that he shouldn't get any extraordinary recognition for it.
where his son's body was thrown and lost with his "n*****s."
To make sure we keep pace with the action in the poem: when he died at the battle of Fort Wagner, Colonel Shaw was buried in a ditch with the dead black infantrymen.
"N*****s" is in quotations because it's not the offensive language of Lowell, or of the speaker, but of the Confederate soldiers who killed them and threw them in a ditch.
Also offensive is the use of the possessive pronoun "his." Of course, Shaw may have lead the African American soldiers, but he certainly didn't own them the way that "his" might suggest. Again, we're seeing his role in the war through Confederate eyes.