Kate (who I like) has pulled out of a high profile event previously (breaking a 115 year tradition of female royals at that event), citing the children and was instead spotted shopping without them (although, she could have had the children later).
Most of the pap photos of Kate are sans children, shopping. The newspapers could twist that if they wanted. When she lived in Wales, sources pushed the idea she was a housewife doing everything herself and was there but she actually had four full time domestic staff and was regularly photographed shopping in London. That could have been twisted too - to suit whatever agenda the newspaper wanted.