If I don't send her am I at fault or do I have just cause to not make her go?
The question of whether a court child custody order is in place was never answered. From the way the OP's question is asked, I will assume that one isn't. If that is the case, you have no obligation to make her go.
Do accused child molesters still get to visit their children unsupervised?
The rule is "innocent until proven guilty. Both parents have shared custody, but, as the saying goes, "possession is 90% of the law.", but there is no law prohibiting an accused parent of unsupervised visitation, absent a court order.