I have a question. Why was it the nephew of Dr. Martin Luther King at the White House

The question shouldn't be why Dr. King's children weren't there. The question should be why was Dr. King's NEPHEW there??!

its the Trump show.

With Trump in the WH, it could get down to someone that once met Dr. King

Some are conservative and want control of the organization and money.
They didn't get it.

They support Trump.

Alveda King, Rev. Dr. Martin Luther King Jr.’s niece and apologist for President Trump has a very long anti-LGBT history. But that stands in sharp contrast to MLK and his equally activist wife, Coretta Scott King, who kept up the Dream long after her husband’s assassination. What history forgets is that Coretta Scott King was a close friend of Bayard Rustin and introduced him to MLK. Indeed, Coretta continued her close relationship with gays through Lynn Cothren, a white gay man who served as her closest assistant for 23 years until her death in 2006. After King’s funeral, the late poet Maya Angelou told this reporter that Cothren had “always been to me like a son. He was a son to Coretta and a son to Betty [Shabazz, widow of Malcolm X], too.” On the fight for LGBT equality she said: “I am aghast and appalled at any people who decide that another group should not have their rights. We’re all each other’s people.”

http://www.losangelesblade.com/2017/08/24/remembering-bayard-rustin-martin-luther-king-jrs-mentor/

that man.

who has long ago been functionally disowned from the rest of the King family. She is a perverted and vile lying hypocrite, who advocates for gestational slavery and the forcible stripping away of 14th Amendment protections from over half of America's citizens. She's also an aggressive homophobe. I'm betting that no ACTUAL King family members would accept an invitation from Shitmouth. Probably never even invited any of them since he knew it would most likely result in very public refusals to attend.

https://rewire.news/ablc/2016/01/22/dont-know-mlk-thought-abortion-neither/

https://jezebel.com/5876611/no-fox-news-martin-luther-king-jr-wasnt-anti-abortion

https://thegrio.com/2010/08/27/mlks-niece-turns-a-beautiful-dream-into-a-nightmare/

On edit: I thought the reference was to Rump's dedication, 2 days ago, of the MLK birthplace as a national historic park. The reprehensible Alveda King was in attendance for that. Now understand that Dr King's nephew, Isaac Newton Farris Jr. attended the signing of the proclamation, which is what this story referred to. At least Farris did make the point of stating, after the ceremony, that Rump is "racially ignorant and racially uninformed".

From Wikipedia:

Alveda King has said, "Mrs. Coretta Scott King knew that her husband, Dr. Martin Luther King Jr., was pro-life" despite his winning the Margaret Sanger Award from Planned Parenthood in 1966.

After civil rights leader Rosa Parks died in 2005, Alveda King claimed Parks was a symbol for the pro-life movement (although she had served on the Board of Advocates of the Planned Parenthood Federation of America).