First Footer of a section overrides the First Footer of another section after the merge. After merging 'Parent' document (with a different First Footer which is empty) with 'Child' document (with explicitly set First Footer), the First Footer of 'Child' overrides the First Footer of 'Parent' after PDF export.

Workaround 1: Disable 'Child' document's 'HasDifferentFirstPageHeaderFooter' and clear its First Footer's value:

Telerik.Windows.Documents.Flow.Model.Section section = child.Sections.First();
section.HasDifferentFirstPageHeaderFooter = false;
section.Footers.First.Blocks.Clear();

parent.Sections.First().Footers.Add(HeaderFooterType.First);