As far as nursing goes, your DIL can wear a tank top with another looser blouse over it, and then lift up the tank top from the bottom up. By lifting up her shirt, versus pulling it down or undoing top buttons, she will be more discreet. Also, has she tried a nursing cover? They are like big aprons that fasten around the mamas neck, and sort of tent out over the baby. They are loose enough that the baby and mama will be covered, but the baby won't necessarily have fabric tightly against her.
This is easy for me to say, but I would say, for the most part, don't go in public, or do so sparingly! I hate shopping anyway, I had my groceries delivered when I was breastfeeding. I ate out a few times and I went into the bathrooms to nurse. I did the same at church. I know women *have the right* to nurse in public, but I was never comfortable with it. If I was visiting family or friends, I went to an unoccupied room.
Ok, so maybe not everyone wants to be at home like I was... At church or other similar events, your DIL can sit in the back. At restaurants, she can sit facing a wall.
Have your DIL "practice" breastfeeding in front of you. You could advise her how to hold the baby and adjust her blouse so that she is discreet. I just saw a mom breastfeeding at the library. She didn't use a blanket and wasn't exposing herself. She did have 2 tops on, and was lifting them up from the bottom to nurse.
As far as dryness goes, I was dry the entire time I was nursing--this is totally normally. They do sell vaginal suppositories if she gets uncomfortable. Also, Evening Primrose Oil is a great vaginal lubricant. I used it when I was pregnant for perineal massage to prevent tearing during delivery. (It worked!) You can buy the gel capsules and break them open to get the oil out, or you can just buy a bottle of the oil, but that is harder to find.
Good luck.