1. I can't find anything on https://wiki.openstreetmap.org/wiki/Multilingual_names discouraging dual naming; in fact, the Canada section appears to recommend dual naming in some cases the case where the dual name appears on signs (like in the Sea-2-Sky). Many places already have dual names present (eg. Estetiwilh / Sigurd).

2. There are many ways to solve this. One could follow signage, more common usage, traditional importance, or perhaps some other rule. 

3. The idea that the "secondary name is not used at all" is quite a bold claim. I am sure that Sḵwx̱wú7mesh speakers call their hometown Sḵwx̱wú7mesh. 

Note: one can just call it Sḵwx̱wú7mesh; "Sḵwx̱wú7mesh sníchim" means 'Squamish language' and is somewhat redundant (though of course it depends on the grammatical construction in Squamish itself)).

I think it's a nice touch for the region in general - I can see the argument of it being toned down and that only specific places of traditional importance be given their indigenous names; for example, Whistler could stay Whistler, being in shared territory where neither nation would permanently reside, and Pemberton can be just Pemberton given that it is usually called Pembert(o)na in Ucwalmícwts (also since Nkwúkwma is the name of a new development in Pemberton and it would reduce confusion). 

But for places like Squamish, and other important sites like Mt Garibaldi, Mt Currie (both the mountain and the town), Joffre Lakes, and Lillooet, just to name a few, I think it would be absolutely appropriate to have dual names.

We could, of course, also contact the nations in question in order to find out their thoughts on naming practices in their traditional territory (and language).