Consider the wording for cleric:
A cleric may attempt to turn undead a number of times per day equal to 3 + his Charisma modifier.
By direct comparison, it seems, as written, like someone with the Glory domain can simply turn undead, period, no “attempt” necessary, so no rolling at all, and can do it as often as they like.
I think we can all agree this isn’t right: the very ability in question gives a bonus on a roll that, according to this literal reading, doesn’t need to be made in the first place. And turning undead at will is something the game would explicitly highlight.
But if that’s not right, what is right? So far as I can tell, we have no other sources of information here—there is the faulty wording of the Glory domain itself, and nothing more to go on. I think most would consider it most plausible that the Glory domain is only giving you a bonus on rolls, and that the ability to actually attempt those rolls has to come from elsewhere—but as you say, that’s a problem because the prestige class is clearly available to non-clerics.
Just to be thorough, the sources for the Glory domain, in chronological order, are:
|Defenders of the Faith
||Any PrC granting extra domains
|Deities & Demigods
||Any domain source
||Any domain source
||Any domain source
The non-core “divine” material in the SRD, including the Glory domain, is a partial, open-game reprint of Deities & Demigods. Note that the hyperlink found on d20srd.org is an addition by the creator of that website—Wizards of the Coast’s publication of the SRD did not include any such link. Only Draconomicon uses the “you turn” wording.
The original source for “prestige domains” was Defenders of the Faith. Its description of prestige domains in general acknowledges that non-clerics can gain access to prestige domains, and while it details exactly how the domain spells work in such a case, all it says about the granted power is that the non-cleric gets them. No clarification on Glory domain’s reference to turn undead is offered.3
Complete Divine doesn’t recognize the concept of “prestige domains,” or any domains available solely through a prestige class, at all. All domains are available to clerics, and others who get domains, normally, including the Glory domain. Complete Divine instead defines new rules for “extra domains” available via prestige class, which are very similar to the rules for “prestige domains” excepting, of course, that they don’t need to be gained via prestige class. Deities & Demigods had already done that for most of the prestige domains in Defenders of the Faith,4 including the Glory domain, but Draconomicon had arguably undone that for the Glory domain when it was reprinted as a prestige domain for the dracolyte.
Spell Compendium’s version of the Glory domain itself is the last publication of the domain, and as such is the “official rule.” However, since Spell Compendium doesn’t have particular rules about how domains are gained or how their granted powers work—it just lists domains in an appendix—really Complete Divine is the last word on the subject of domains from prestige classes. The wording of the Glory domain’s granted power is the same in Spell Compendium as it is everywhere else, aside from Draconomicon.
It is probably worth noting that Complete Divine specifies that for those prestige classes that offer an extra domain that isn’t specified by the class, “a character can choose from any domains offered by his deity (or can choose any domain if he doesn’t worship a specific god).” That doesn’t help favored souls,5 but for others it could be useful. For a favored soul, though, one must take a prestige class offering an extra domain while worshiping Heironeous, Pelor, or Re-Horakhty, or else take the dracolyte prestige class specifically,1 in order to access the Glory domain.
So the only real answer we have is “we don’t know; probably not?” After all, the biggest reason to doubt that the Glory domain is purely a bonus is that all good dracolytes are forced to get it even if they can’t turn undead, but if you consider it in its original context—Defenders of the Faith, where it was just one option among many—that interpretation seems much more plausible. But still, I’d suggest a lot of salt to go with that claim.
Ultimately, this is a question that simply has to be taken to a DM. At which point you should probably just have a conversation with the DM about fixing the favored soul in general, rather than relying on a poorly-worded domain to kinda-sorta do the job, but only later in the game, and then worry about whether other classes can also get access to turning that way and whether or not that’s a problem. After all, Complete Divine actually makes the Glory domain dramatically more accessible to non-favored souls, since they would have other non-dracolyte, non-Heironeous/Pelor/Re-Horakhty options for the domain.
Though Draconomicon says “A dracolyte is [...] a divine spellcaster who devotes his energy and support to the deities of dragonkind,” pg. 122, nothing in the actual rules requires a dracolyte to worship any particular deity, draconic or otherwise. YMMV.
Spell Compendium does not list deities associated with any of the domains it lists in Appendix: Domain Spells, so nothing should be read into its absence for the Glory domain.
Despite the fact that Defenders of the Faith has an explicit “Granted Power Note” sidebar, it still doesn’t explain the Glory domain’s granted power—that sidebar instead attempts to justify why the Creation and Divination domains grant a +2 bonus to caster levels instead of +1.
“Several of the domains presented in this section—Community, Creation, Glory, and Madness—originally appeared as ‘prestige domains’ in Defenders of the Faith. They are presented here as standard domains for some deities who appear in this book.” —Deities & Demigods pg. 213.
“Unlike clerics, favored souls are not able to devote themselves to a cause or a source of divine power instead of a deity.” —Complete Divine pg. 7.