The premise that William the Conqueror was distinctly "kind" at Dover but "cruel" on his march to London lacks solid historical evidence. While William's invasion of England in 1066 and his victory at the Battle of Hastings are well-documented, contemporary chronicles do not support a sharp behavioral contrast between his actions at Dover and his subsequent advance.
After Hastings (October 14, 1066), William moved to secure the strategic port of Dover. The garrison there surrendered without a fight. William stayed for a week, building fortifications (the precursor to Dover Castle) and resting his army. There are no records of exceptional clemency or brutality during this occupation—it was a standard military consolidation.
William then advanced toward London, harrying the countryside (a common medieval tactic to deny resources to the enemy and intimidate submission). He crossed the Thames at Wallingford, received the submission of Stigand (Archbishop of Canterbury) and other nobles at Berkhamsted, and was crowned in Westminster Abbey on Christmas Day 1066.
The extreme brutality associated with William's reign occurred years later, during the Harrying of the North—a scorched-earth campaign to crush rebellion in Yorkshire and the North East. This involved widespread destruction, famine, and death. It was not part of his 1066 march from Dover to London.
In short, William was a pragmatic, often ruthless conqueror throughout. The Dover-to-London march was a calculated military advance, not a shift from kindness to cruelty.