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For example, in black and white there is a trainer wanting a boldore and trading an emolga for it. So, if I were to catch a modest boldore with nice DVs, would the emolga also be modest and have nice DVs?


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No. The IVs of the Pokemon you get through in-game trades are fixed, which means their nature is fixed too.

Here's what's great though - in Black/White all the IVs are 20, except for one which is maxed out at 31. So you get a pretty good Pokemon.

Here are the Pokemon you can get, with their maxed IVs:
Petilil or Cottonee: 31 SpAtk
Basculin: 31 Atk
Emolga: 31 Def
Rotom: 31 SpDef
Munchlax: 31 HP

My question was more of concerning the EVs so it would make getting certain pokemon with nice stats easier.
Well, this night this question became unnecessary because I captured a modest boldore and got a lax emolga >.<
Luckily I saved before doing this (afk time to free that damn boldore)