It isn't actually possible to trade with DESMUME, since Nintendo uses a separate connection signal
(NWIFI or something). You can patch ROMs to trade as seen in some hacks. Because Emerald is an older version, I don't think that would work anyway, because normally on a handheld both cartridges would be in at once. The only way is to use cheat codes to get the Pokemon you want, rare candies, and TMs if needed.
I use gpSPhone on my iPad and iPod, because I don't like the size of computers. Sometimes I will use DESMUME because the newer gens are not compatible.