A week before the Hamptons fund-raiser, on July 25, Mr. Trump stunned one of his wealthiest patrons, Miriam Adelson, the widow of the casino magnate Sheldon Adelson, by having an aide, Natalie Harp, fire off a series of angry text messages to Mrs. Adelson in Mr. Trump’s name, according to three people with knowledge of what took place.

The texts were particularly jarring because Mrs. Adelson and Mr. Trump had a friendly meeting just a week earlier at the Republican National Convention, according to a person briefed on the matter. The texts complained about the people running Mrs. Adelson’s super PAC, Preserve America, into which she is pouring millions of dollars to support Mr. Trump.

At the time, Preserve America was spending nearly $18 million on a week’s worth of ads aiding Mr. Trump in three battleground states. The texts said that the officials running Preserve America were “RINOs” — Republicans in name only — and that Mrs. Adelson’s late husband would never have tolerated that, the people said.

According to two of the people, aides to Mrs. Adelson later discovered that the outburst against her had been encouraged by another major Trump donor, Ike Perlmutter, the former chairman of Marvel Entertainment, who had hoped in vain that Mrs. Adelson would contribute to a rival super PAC that he backs.

They are starting to eat their own.