WASHINGTON — The Republican-controlled Congress opened the turbulent Trump era in Washington on Tuesday, as the new Senate moved instantly to begin the repeal of President Obama’s signature health care law while the House descended into chaos in an ill-fated attempt to gut an independent congressional ethics office.

On a day usually reserved for pomp, constitutionally mandated procedure and small children parading around in fancy dresses, Congress instead pitched itself into partisan battles.

Speaker Paul D. Ryan easily won re-election, but not before the embarrassment of having his members defy him by voting to eliminate the ethics office, only to then abandon that effort after a flood of criticism from constituents and Twitter messages from President-elect Donald J. Trump that criticized House Republican priorities.

It was a rocky start to a period in which Republicans had promised an end to Washington gridlock if they controlled both Congress and the White House. There was intraparty conflict and a sense that Mr. Trump, who ran against the Republican establishment, would continue to be openly critical of his own party at times.