It was an issue in the Zimmerman case. It prevented an immediate arrest and collection of evidence/interviews which may have been fruitful, and more importantly, the jury was given instructions specifically pulled from the statute, which jurors identified as being a factor in their decision. (And it may have influenced Zimmerman's calculus to be armed and go around following people).
As for Sybrina Fulton being in Washington, that has nothing to do with Obama. She was there for a Senate Judicial Committee hearing, specifically the Subcomiittee on The Constitution, Civil Rights and Human Rights, headed by Dick Durbin (a white man).
Is the Stand Your Ground laws a racial issue? I don't know, but many believe it is, hence, I would guess, is the reason for inviting mothers who have lost sons who are a protected class of citizens. Should blacks be a protected class? Yes, they were once bought and sold as cattle and still to this day face racial animosity and prejudice.