Unfortunately, I do not think that yEd offers a layout algorithm that is very well-suited for the kind of diagrams you want to create.
You could try yEd's hierarchic layout. However, that is a general purpose algorithm that has no special notion of families or individuals like the family tree algorithm has. If you go that route, try the following approach:
Create your diagram.
Run hierarchic layout with options "Select Elements Incrementally" und "Use Drawing As Sketch" on tab "General" disabled.
Manually adjust the positioning of families.
Run hierarchic layout a second time, but with "Use Drawing As Sketch" enabled.
In step 3, your modifications do not need to be pixel perfect - they just need to be roughly at the right position. The second run of the algorithm will result in nice alignments.