I know there seems to be a lot of curiosity surrounding the Amish -- trust me, I see all the tourists clogging the streets where I live! And if a horrendous rumor were started (i.e. they "share" their daughters with uncles and elders of the church, etc.) the Amish would never refute it, even if it were false. That's not their way. They would say nothing.
Aside from the fact that they don't use electricity, in many respects, they're pretty much like you and me. They cry when they're sad; they get depressed; they work hard; they like to have fun; family is important to them; they pay property taxes; they help out their neighbors; they discipline their children; they fall in love; they get married; they die. I was in the hospital with my son once, and there was an Amish family whose child had just died. Never in my life have I heard such heartbreaking sobbing and keening as I did then. When you cut them, they bleed, just like us. They rely tremendously on their faith, and tend to turn the other cheek when harrassed or hurt by the actions of others.
Yes, I'm sure there are instances of spousal abuse, child abuse; abusing alcohol (especially among those under 25); and, as we've seen recently, even murder, as well as a host of other ills that plague society nowadays.
I would agree that the rate of abuse is similar to the rest of us, possibly even a tad lower.
I know some will argue that they have higher rates of mental illness, mental retardation, physical birth defects, due to "intermarrying". And that may well be the case, (to be honest, I'm not really sure); but that's a whole different thread topic.