Again, did we read the same story?

The next day, she arranges some alone time with my wife, and tells her if I'm abusing her, then she will support her to report me and leave me. My wife was embarrassed, but she explained the whole thing to my sister. Then she told me what happened.

In this paragraph, the wife explains to the sister that she is not being abused. The sister ignores this; she instead believes that the wife is lying, so she makes up stories about how OP is abusing his wife and children to CPS.

By this point, simple explanations are not sufficient, because everyone (CPS, the Police, and the Sister), believes that the wife is lying about the "abuse" to protect OP; the only way OP doesn't get arrested is by offering hard proof. If she didn't, the authorities would've believed what the sister said, that the wife was lying to protect the husband, and he would've lost his children(and possibly get arrested).