For a few kids, the cut off for National Merit Semifinalist might matter. I think historically the DC cut off is higher than for MD.
DC tag has an upper income limit. I think it’s currently about $600,000. I don’t know the rules for divorce.
You get a small amount–I think it’s $2,000 a year–for private schools in DC. HCBUs also get you a grant–I think it’s $10,000.