As a class feature, a paladin's mount does not have a challenge rating, since it's already factored into the Paladin's challenge rating The same applies to animal companions and familiars. While it is never explicitly stated, defaulting to the person whose class feature they are does make sense in circumstances like these.

As such, Paladin's CR +5 seems like the logical conclusion but this is a situation that doesn't seem to be covered by the rules, despite that it should probably have been. By a very strict reading of the rules, they would probably gain a spell resistance of 5, which at level 11 is useless.

Either way, it's obviated just a few levels later (as you pointed out) and barring an official ruling or erratum somewhere, Paladin's CR +5 seems the closest to the rules option we have available.

Your DM is correct: it does provoke an AoO.

The confusion here comes from your reading of the sentence where you believe that the second part only applies if the first is true. The sentence is in fact a two item list; the first half and second half do not interact with each other in any way.

The d20pfsrd also says

A spell-like ability has a casting time of 1 standard action unless noted otherwise in the ability or spell description. In all other ways, a spell-like ability functions just like a spell.

And spells provoke (except when cast as a swift action).

Interesting, you can Arcane Bloodrage defensively, since you have not actually entered a bloodrage when you apply the effect, it is done as part of the activation.

This is the RAW on the matter. The fact that swift action spells do not provoke does not mean that free action spells or spell-likes do not, though it is certainly worth making that point when discussing this with your DM. (Especially since the reason is that there are no free action spells any more is, to the best of my knowledge, because when pathfinder came out it had turned them all into swift actions)