Gating in and naming
Gate seems like it should get you inside a Mord's Mansion.
The gate spell says that it creates an opening "between your plane of exitence and the plane desired". Later it says in the gate's Planar Travel section that "the gate open precisely at the point your desire". There is *one* line about it appearing "into the plane you named" and that's the only mention of naming (other than calling in a creature). That seems pretty clearly to be flavor text; I believe the intent of the spell is to let you open up a plane to any known location (much like scrying), rather than to call out a verbal, naming description "I open a gate to Intrope's Mord's Mansion that he created in the Piratecat mountains five hours ago!".
Plane Shift is a tougher call. I guess if I'd personally allow, say, a limited wish (300 xp to cast!) to create the proper planar key focus and then allow plane shift to work. I'd say, again, the intent of being off a number of miles is assuming the plane is much larger than that; the spell description says that you can't get pinpoint accuracy. So I'd allow a plane shift in, but they'd appear in a random room!
I scanned through my copy of Manual of the Planes. I had totally forgotten that in all the planar goodness that they squeezed between those covers they gave us NOTHING about bags of holding, Mord's mansions, or other extradimensional things. I was hoping for a small section to address just these kinds of issues. Oh well. Can't have everything, right?