My father always tells me that Hitler was more restrained in fighting the British because they were cousins to the Germanic people as opposed to, say, the Slavs. Is there any truth in this?

In Nazi racial theory, the British — along with the French, Dutch, Scandinavians and other northern/western European ethnic groups — were regarded as part of the Aryan race (though not, of course, the 'pure' Nordic German ideal.) The Nazi view of race certainly didn't treat these non-German Aryans with anything like the contempt and dehumanising fervour that characterised their attitudes towards the Slavic, Jewish and Romani peoples.

But Hitler's personal views on Britain were complex, and evolved over time — they were heavily coloured by the memory of the First World War and the tense relationship between Britain (as an old-world superpower) and Germany (as a rising imperial power) in the late 19th/early 20th century.

Here's Ian Kershaw, one of the great biographers of Hitler, on Hitler's political/foreign policy views in the early 1920s:

Hitler’s early views on foreign policy were conventionally pan-German. They were no different from those of many nationalist hotheads. In fact, in essence (if not in the extreme way they were advanced) they accorded with a revisionism that enjoyed wide popular backing. Nor, in his emphasis on military might to overthrow Versailles and defeat France, however unrealistic it sounded in the early 1920s, did he differ from many others on the Pan-German and völkisch Right. [...] By late 1922, an alliance with Britain, whose world empire he admired, was in his mind. This idea had sharpened in 1923 when the disagreements of the British and French over the Ruhr occupation became clear.

But by 1937:

Hitler’s belief in an alliance with Britain had by now almost evaporated. His attitude towards Britain had come to resemble that of a lover spurned. Contemptuous of the British government, he also saw Britain greatly weakened as a world power. Egged on by Ribbentrop, by now aggressively anti-British, his hopes rested on his new friend Mussolini.

Source: Ian Kershaw, Hitler (2009).

There's also some interesting insight from Hitler himself in Hitler's Table Talk — a compiled volume of his monologues and diatribes recorded by members of his inner circle. The entry from the night of 22-23 July 1941 focuses heavily on his view of German relations with Britain:

The Englishman is superior to the German in one respect— that of pride. Only the man who knows how to give orders has pride.

[...]

As soon as we started our economic ascent, England's doom was sealed. It is quite certain that in future England's Empire won't be able to exist without the support of Germany. I believe that the end of this war will mark the beginning of a durable friendship with England. But first we must give her the k.o.—for only so can we live at peace with her, and the Englishman can only respect someone who has first knocked him out.

The memory of 1918 must be obliterated.

Source: Norman Cameron & R.H. Stevens, trans., Hitler's Table Talk 1941-1944: His Private Conversations (2000).

As well as race, Hitler was obsessed with class and empire — he talks a lot in that text about India, and the failures of the British class system and colonial administration. There's a measure of admiration there, but there's also a distinct and consistent sense that Britain is the 'old world', and that their role in the new Germanic order would be much diminished.

So, to answer your question in a circuitous sort of way: yes, Hitler had a certain regard for Britain, and he certainly wasn't proposing its obliteration or the extermination of its people — but I'm not sure it's the case that he fought any less zeal against them as a result of that; actually, I think he regarded Britain as one of his most dangerous enemies.

Edit: cleaned up syntax.