Q:

How do I rationalize this interesting chord in Mozart K. 331?

Lately I've started learning some basic music theory and I have been trying to rationalize some of the interesting chords I have heard of from famous pieces. Here is an example of which I am not sure if my understanding is correct.
Below are bar 11-12 from Mozart's Piano Sonata No.11 in A major, K.331. I have marked the chords using Roman numeral notations.

The blue text shows a naive marking. To me the ♯iv° chord gives a warm and sweet shifting feeling. I found that if I think of it as an applied chord (by tonicizing V) then the last three chords becomes a (vii° - IV - I) progression. If this is the case I was wondering how come the IV chord, as a pre-dominant chord, appears after the dominant chord vii° instead of before it? Why would the progression still sound inevitable when the strong dominant -> tonic progression is broken? 

Per @Dekkadeci's answer I revised the analysis as follows. The final three-chord progression simultaneously resolves two tension (cadential I chord to V, and on the V scale, dominant vii° to tonic I.

A:

If this is the case I was wondering how come the IV chord, as a pre-dominant chord, appears after the dominant chord vii° instead of before it? Why would the progression still sound inevitable when the strong dominant -> tonic progression is broken?

Due to the E as a root instead of an A, the second last chord is not formally a I or a plain IV/V chord, but it is actually a I 6/4 chord. The I 6/4 chord is treated as a pre-dominant chord that must be immediately followed by a dominant-function chord (often V, just like the last chord). Its pre-dominant function is so strong that one of the theory books I was told to use in harmony class labels it as V 6/4 instead.
(I also believe that the "#iv° 6" is actually vii° 6 of V.)

A:

You ask how to rationalise the progression.  Here's how.  It's a bare-bones B7, the dominant of the following chord, E, to which it resolves, delayed by a suspension.  There's no room for all the notes of B7 in 3-part texture, but that's no reason to analyse it as something unnecessarily complicated.

