The Bush family wants to keep services honoring former President George H.W. Bush about his life and accomplishments, avoiding the type of politics that were on display at the late Sen.
Trump's relations with the Republican establishment have been rocky since his insurgent campaign took him to the party's nomination and then a shock election win in 2016.
Despite Dole, a longtime U.S. senator from Kansas, challenging Bush for the Republican nomination in the 1988 presidential race, the two men remained friendly.
Controversial as a politician, the 41st president has been feted in death as the embodiment of a public servant - with some of the commemorations pointedly contrasting him with the current White House occupant. So, the Bush family is staying in the home while they await the elder Bush's funeral at the Washington National Cathedral Wednesday.
Bush is the 11th president to lie in state at the Capitol and among 31 people to have been given the honor.
The Kansas Republican, 95, who like Bush was a decorated veteran from his service in World War II, was the Republican presidential nominee in 1996 against President Clinton.
As official Washington paid its respects inside the Capitol, Americans queued up outside the Capitol Visitor Center for their chance. "During his presidency, national and world leaders came to Walker's Point to address issues of national and worldwide importance in the peaceful and handsome setting of the ME coast in the summer", he said.
The 41st President's spokesman Jim McGrath also commented via Twitter, saying the moment was: "A last, powerful gesture of respect from one member of the Greatest Generation". As a candidate, Trump belittled Bush's son Jeb, a Republican rival for the presidency, and has long criticised the Iraq War launched by George W. Bush.
The furry friend traveled the many miles from Texas to Washington D.C.to attend the open casket service, alongside the Bush family. Flags on public buildings are flying at half-staff for 30 days out of respect for Bush.