The source for the Catherine/Peter the Great interpretation can be found in Massie's "Peter the Great."
The issue was not entirely the infanticide. The issue was that Peter had issued a ukase stating that there would be no infanticide [then a common practice] because Russia at that time was relatively underpopulated. Having enforced the law against the common people, he could not excuse an event that Mary Hamilton had performed more than once, including at least once after the issuance of the order.
Apparently, she was quite a bawdy lady.