Many people cough a lot when they try their first e-cigarettes. The vapor is different from cigarette smoke, and like when we first tried cigarettes, it takes a little while for our bodies to get used to vaping.
Having something to drink while vaping is a good idea and will help the initial dry throat and coughing. Smaller, gentler, and less deep inhalations will work, too. Not sure how she inhales her cigarette, but with vaping it is recommended to suck the vapor into the mouth as if you are sucking on a milkshake, not directly into the lungs. Then she can either inhale into the lungs, or exhale through both the mouth and nose. (Exhaling some vapor through the nose helps you "taste" the flavor in vapor.)
The molecules in vapor are a different size than the molecules in smoke. Most of the nicotine in vapor will be absorbed in the mouth and throat, very little in the lungs. So from a nicotine absorbtion perspective, it is not neccessary to inhale vapor to get your nicotine delivery.
Over my 8 months of vaping, I have found that I prefer a "cooler vape". My juice delivery devices (cartomizer, cartotanks, etc) use a standard resistance heating coil (3.0 ohm), which do not create what I experience as a harsh vapor like the low resistance (1.5 - 2.0 ohm resistance) cartomizers make. So your wife might need to try a cartomizer or clearomizer that has a higher ohm rating for a cooler vape.