A councillor described disputes over bilingual signage and flags as a "vicious circle".
Three people have been arrested after disorder broke out near the Broadway roundabout on Saturday, police say.
Some MLAs are considering leaving elected politics over the abuse they and their families face, BBC News NI understands.
The three-acre site near the City Hospital contains more than 10,000 bodies dating back to the Irish famine.
SDLP leader Claire Hanna says the event in the US capital was "largely a glass-clinking and selfie-taking opportunity".
The assembly speaker told MLAs sittings of the assembly "are not just another engagement in their diaries".
Northern Ireland needs two new Irish language post-primary schools to meet the demand, according to the EA.
The Education Minister Paul Givan has declined 205 meetings since taking office.
The rioting involved about 40 people, most of them young teens, the PSNI said.
