We all have those kiddos who don't get support from home, for sure, and I "feel your pain".
One idea we have tried is to find "in-house" mentors for those kids. It can be teachers who are willing to give up even 10 minutes of their planning time a few times a week, as well as our secretaries, custodians and counselors.
Another way we've found "listeners" is to have Buddy Classes, where 5th graders and 3rd graders, 4th and 1st, 2nd and Kdg (or how ever it works out for you) have a time each week when the older kids both read to and listen to their younger partners.
It's difficult to change habits at home, but we can find extra support at school.