Learn English – “Inside” vs. “on the inside”

'Will' is a modal verb and 'be going to' is its phrasal modal counterpart. Such verbs work for epistemological uses (logical/deductive) and for deontic (social/interactive) uses. The first question is about a social use here, a kind of promise that the hotel clerk is making. The choice of the phrasal modal 'be going to' indicates that the clerk's plan is already 'afoot' -- in other words, it conveys to the clients that their problem is half solved already, no doubts, no conditionality, just as if the solution HAD been planned yesterday and we were in the middle of carrying the plan out.

So, Totoro, I think what you have discovered is that when 'be going to' is chosen over 'will' in a situation like this one, the speaker is inviting the listener to feel as if he/she has been part of the speaker's thoughts for much longer than the spontaneous moment. That is good business discourse.

The second use in the dialog is screamingly artificial (and uses 'in' for 'on' to boot).

In Standard English, inside is followed by of when it’s a noun, so you might say, for example, ‘I’ve never seen the inside of a prison.’ When it’s used as a preposition of is not required, so you can say ‘I’ve never been inside a prison.’ However, in non-standard speech, of is sometimes found even in that sort of construction.