Sorry for not answering your comment, I remember reading it in the comment section. start_pos_characters and start_pos_family_relationships are the only tables you need. The problem is how the family trees work. The characters that will be shown in the family tree are determined according to the following rules:
1) Only the direct descendants of the original faction leader are included in the tree. Ascendants or side family members of the original faction leader will not be included.
2) Spouses and their descendants from other marriages will be included as long as they remain married to a character of your family. If your family member dies, they will stop being part of the family tree.
3) If a family member is transferred to another faction (for example through marriage), they and their spouse will remain in your family tree, but their descendants will be left out.

Your problem lies in rule 1, Atreus and Menelaus are not direct descendants of Agamemnon. You need to define Atreus as faction leader in start_pos_characters (remember to remove Agamemnon). If you wish, you can kill Atreus through commands (check the script in my mod).

Thank you, now it makes sense! I'm used to modding TW Three Kingdoms so didn't realize that the family tree displays follow different rules here in Dynasties. Cheers!

It took me some trial and error to figure it out, I probably was the only person who knew this until now

Hmm, I'm now getting a startpos compiling error when I simply switch the faction_leader entry from Agamemnon to Atreus, keeping everything else the same. Was there any other tables or dependencies that need to change?

No other tables are necessary. Some possible issue might be:
1) Make sure that every faction has exactly 1 faction leader. Maybe you added Atreus to the wrong faction (some factions have a Pharaoh and a Dynasty version).
2) The faction leader needs to be spawned in the campaign map. Do not set the pawn coordinates (startx, starty) to -1, -1.
3) Leave the "Death type" and "Turns died before start" empty, your faction leader should be alive when the campaign is created.
4) I don't know if this is necessary, but just in case use a generic entry for the Override general unit column for Atreus, not a special one like the one Agamemnon or Menelaus use. I would copy the entries of Orestes and use those as a reference for Atreus, plus the faction leader entry.

Ah, that's probably the issue then - I had him off the map with coordinates -1, -1. Thanks again! Hopefully it works this time.

It worked! Though is there any way to script it so Agamemnon can keep his court position when his dad dies?

Nice

I have updated the mod to fix this issue, the phar_court.lua script allows you to directly select Agamemnon as Mycenian heqetas

My props to you sir

Cheers!