Okay, thanks, that helped. It looks like your "Diplomatic Relations" score with a country is the same as your "Their opinion of you" score, but only if you've got a diplomat sent over to them (I think?) Otherwise, you have no "Diplomatic Relations" score with them, regardless of what your "Their opinion of you" score might be.
Sounds right?
No, no, no. You are confusing several subjects here. "Diplomatic Relations" is not a
score.
"Diplomatic Relations" is the number of slots you have available to maintain interactions with other countries without penalty. The default starting amount is 4. Every instance of alliance, marriage, military access, personal union, vassalage, or guaranteeing with a unique nation occupies one slot. Allying four nations means you are using 4 / 4 relations slots. Allying AND marrying one nation does not add a slot used beyond 1. Therefore, if you ally AND marry the same 4 nations, you are still using 4 / 4. If you asked them all for military access, you are still using 4 / 4. However, if you allied, married, OR asked for military access from another nation, you would be at 5 / 4 and receive a -1 diplo point / month penalty. If you allied one nation, had access from a second, and married a third, you would be at 3 / 4 slots used.
Diplomacy idea set adds +2 relations. Expansion idea set adds +2 relations. Becoming Emperor of the HRE adds +2 relations. Various countries (France, Milan, Savoy) have +relations as a national idea.
Every slot you occupy above your limit gives a cumulative -1 diplo point per month income. There is no upper bound to how many relations you can have, but if you maintain too many, you'll have no diplo point income at all.
"Relations" itself means your
opinion of a nation or theirs of you. This is completely independent of diplomatic relations. You could easily end up using a relations
slot from a country that hates your guts (example : you married a nation early on, but then become their biggest rival), and you might be on good terms with a nation (+25 religion, +100 boosted relations) but have no diplomatic relations slots used (because you haven't allied, married, or gotten access from them)