:True, you won't find many sources equating Urdu with Hindustani today. This was usage of the nineteenth century and earlier. However, you repeatedly say that Hindustani is 'derived' from Urdu, or a 'mix' of Urdu and Hindi. I have seen this description only in very simplified accounts, where the author doesn't want to confuse the reader by going into details. Also, it is likely to be the common conception of Hindustani speakers, for their point of reference is now the standardized languages of modern standard Urdu and modern standard Hindi, rather than the colloquial language which gave rise to them in the first place. Otherwise it seems clear, from all sources, that Urdu and Hindi are standardized registers of Hindustani - that is, that Hindustani as presently conceived (as the vernacular language of Delhi and surrounding areas, or the lingua franca of northern India & Pakistan) is the basis for both modern standard Urdu and modern standard Hindi.  

 :As for Hindustani being influenced by Urdu and Hindi, of course this is going to happen. Whenever people are educated under a standard language, or exposed to a standard language through television, radio, or cinema, it will influence their colloquial speech. You see this all over the world, where the differences between regional dialects disappear under the influence of the standard dialect. This is true for English, German, French, Japanese, Chinese, Malay, Italian, Russian, etc etc etc. This only thing that makes Hindustani unique is that it's being pulled in two directions at once. But that doesn't mean that its origin is in the standard languages! Quite the opposite: standard languages are in every instance colloquial dialects that were cultivated for official use. Hindustani is different in that it was a lingua franca that was cultivated for two official uses, modern standard Urdu and modern standard Hindi.