Leicester Crown court heard Ian Walters, 51, from Swindon, drove purposefully off the M1 after a 'make or break' holiday with his wife Tracy to Yorkshire.
Mr Walters, who served at Christ Church in Swindon, denies murder.
His wife was unable to cope with his constant sexual demands, and the couple had a 'troubled' relationship the court was told.
Charles Miskin QC, prosecuting said Mrs Walters had asked for divorce on multiple occasions and her husband had been violent in the past. He continued, saying during one violent episode, weeks before her death, Mrs Walters had locked herself in the bathroom and phoned the police.
When officers arrived Mr Walters had denied being violent but admitted he had been 'annoyed' that his wife had refused sex.
During their holiday to the Yorkshire Dales, the court was told Mrs Walters made an 'unconnected' 999 call to police from their cottage.
Mr Miskin said tests show the weather and road surface were 'good' during the journey home and technical experts found no problems with the vehicle. He told jurors that Mr Walters had crashed "because he wanted to show her who was in charge, who was in control."
Mr Walters left the M1 at Markfield, Leicestershire travelling at around 74to 84mph.
The pair both worked as driving instructors in their home town.
The trial continues at Leicester Crown Court.
