[Formendacil]

Let's imagine, for one absurdly out-of-character second, that Aragorn WOULD have considered "arresting Gandalf" and/or asserting himself as the mutinous new leader of the company. Even had he already become King of Gondor and Arnor, or had the quest somehow waited until he was, this would still, as Aiwendil so succinctly put it, none of the authority required to arrest Gandalf.

Authority, never mind the actual ability.

Gandalf was a subject of neither the Kingdom of Arnor nor Gondor, over which Aragorn's writ extended. He was, in point of fact, an emissary of the Valar, which, if we continue this line of thought, still leaves him a foreign national--and a foreign national rather in the diplomatic service.

Beyond this, when at the walls of Moria, the company was not in the realms of Gondor or Arnor. Depending on where one draws the exact line, they were either still in Hollin or they were across the threshold into Moria. If one takes the first position, which I incline towards, then they were in what was essentially noman's land.

I seem to recall it being suggested (I cannot recall the text--possibly the Epilogue?) that, by his marriage to Arwen, Aragorn's heirs would inherit the remaining tracts of land still belonging to the High Elves in Middle-earth, namely Lindon, Rivendell, and Eregion (all under the possession of the House of Finwë, which would be remain solely represented in her heirs after the passing of Elrond, Galadriel, and the eventually death/passing of Elladan and Elrohir).

However, this had not happened at the time of the Fellowship. Hollin was still, at that time, a vacant kingdom under either the nominal lordship of the Heir of Celebrimbor (presumably Elrond, the next-of-kin as the nearest descendent of Fingolfin, who was Fëanor's heir after the exhaustion of his own line) or would have been kingdomless, but part of the greater domains of the High King of Eldar (depending on the tradition one accepts for Gil-galad's parentage, either Elrond or Galadriel). Either way, it is clear from the officially defined boundaries of Arnor--themselves not set until half an Age after the fall of Eregion, that Hollin was considered beyond-the-borders of Arnor, and thus outside the law of her king.

If, however, we stretch the borders of Khazad-dûm beyond the doors to include the doorstep, Aragorn is STILL not king of that land, and even less likely to rule it, since I don't think he was going to be a polygamous king with a second consort wedded to the only daughter of Thorin III (and that's assuming that Dwarves can inherit through the female line--people seem to assume this of Fíli and Kíli, but I don't recall it ever saying in any text that Thorin Oakenshield's sister-sons were the Heirs of the Durin after him).

Gimli, perhaps, as the ranking Dwarf (in all Moria, though they did not know it) could have done so, but we all know that he was on Gandalf's side for going IN to Moria.