Green peppers can be harsh simply because they're picked when they're unripe, and sold before they're ripe. The reason they are so much less expensive than red, yellow, or orange bell peppers is that they're picked quickly, and don't require as much care and tending-to.
They're a quick turn-around crop, whereas allowing the other peppers to mature, turn color, and then pick and ship requires much more labor, and time, and usage of the land. A green pepper that's allowed to remain on the stem of the plant will turn red, yellow or orange, depending on its variety.
So, think of eating a green banana, or unripe blueberries (my dad used to love to say "blueberries are red when they're green"), or an avocado that's not ripe yet. The fruit is tough, sometimes unpleasantly bitter, and it can be hard to digest because it's still young. Raw red, yellow or orange peppers are often much easier on the digestive tract.
A yellow or orange or red pepper is simply a grown-up green pepper. Eaten raw, they can be much easier to digest. Find a green pepper in a grocery store that's turning red. Show your daughter a green banana and let it sit in your kitchen for a couple of days until it turns into a beautiful yellow. Then encourage her to try red bell peppers.