Hi, Todd
re: "moving" children
The easiest method is to 'Edit' the profile of the child (either full Profile or Tree View will work), select the Relationships tab. Then, in the top-most field for the parents you should be able to 'pop-down' a selection list of "nearby" relationships -- select the proper one, then "Save" the results.
If you do that before creating temporary duplication children, then there would be no need to merge.
Otherwise, after moving the children to the proper parents, merge the duplicates. (From Tree View, select, say, the mother's "more" tiny menu item and then select "Resolve Duplicates" from that little menu.)
Hint: be sure to check the "Timeline" tab of the mothers/parents to make sure the children are separated out correctly!
re: preventing
It you can give specific links when something like this happens (e.g.: to the Ancestry 'source' page and to the Geni profile that was the 'focus' profile), then it can be looked at in more detail.
Not specific to Ancestry, I do know that sometimes I'll forget to select the 'update' of a spouse that already exists on Geni, and for each of the children, to check the spouse to which it is to be added (should be a 'popup list' if SmartCopy recognizes there is more than one possibility).
It may also be that the Ancestry data did not have the correct parentage for the children -- that's why specific links can be *really* helpful.