the meaning of "alloy" in Jane Austen's Emma Chapter I

It seems odd, doesn't it? But really, it's a very similar meaning to alloy in the context of a mixture of metals.

The missing piece is that alloy was often used metaphorically in a negative sense to mean that something pure was mixed with something base, a little like we might say "muddy". So to alloy is to stain or to taint.

Her disposition tended to threaten to taint her enjoyments.

Weaken, soften, or make less valuable. Alloy (v.) is usually used to refer to the process of combining two metals so that the resulting alloy (n.) is in some way intermediate in characteristics between the two (although sometimes the alloy has characteristics that neither metal has, as is true with bronze being stronger than copper or tin). As for the metaphor: if you imagine that her "many enjoyments" are gold, and the power of having too much her own way were silver, the resulting alloy, electrum, would be slightly less valuable than gold.