There obviously was a bitter, professional rivalry between Witte Corneliszoon de With and Maarten Harpertszoon Tromp. They were very close in age, born a year apart. Tromp's career was given a boost by him being flag captain for Piet Hein for the Silver Fleet operation.
Witte de With was also known as having a raging temper, and was not personally liked. However, he was also trusted with important commands, because he was known to be a good commander. For example, Witte de With commanded the big operation in 1645 to force a large fleet of merchantment past the Danes without paying the toll.
When the Zeelanders were pressing for someone to rescue their failing venture in Brazil, Witte de With was also sent. In this case, he was set up in a no-win situation. He was sent with a small fleet, with no logistical support. They fought a small battle and took losses due to a Portuguese captain who blew up his ship. When they returned from the debacle, after some crews mutinied, they imprisoned Witte de With. Prince Willem II was ready to have him executed. He was saved after the incident when Willem II died.
The First Anglo-Dutch War was a case where Witte de With was trusted with a great deal of responsibility, but was greatly disliked by the Orangists/Royalists for his Republican stance. They also disliked his no-nonsense approach to timidity or outright cowardice.
At the Battle of the Kentish Knock, Tromp supporters wouldn't let Witte de With on board the Brederode, even though it had been his flagship for most of the time since 1645.
I will write more on this subject, later.
