Since it's very rare for such serious morning sickness, I'm assuming that since William is half-reptilian (because of his mother being non-full reptilian (or non-reptilian at all)-the cause of her death), him mating with apure reptile with reptilian blood (she's part of the blood line as some sort of cousin may cause Kate to reject the child of a non-full reptilian father, similar to the human body rejecting a foreign object in its womb.

For example, would a lizard give birth to a human foetus or simply reject it because it is foreign? Vice versa.

Seems a plausible explanation to me. Morning sickness is an automated response from the body which is caused as a result of the body wanting to reject something foreign, but in normal humans this subsides later on as the body realises it is a foetus.