Well, they kind of hate each other, so it’s pretty hard to make them like you. And - at least on VH (might be different on other difficulty levels… not sure), there is no way you can build up the Empire without making them pissed off, because every “level” of power you increase gives you a malus, topping out at, IIRC, at -60. I could spend a ton of prestige to cancel that out temporarily, but that would mean not having prestige available for events, which is far more important.
The other thing, of course, is that doing anything to help them, will frequently result in you being forced to trespass, which pisses them off - so any benefits you gain from defeating their enemies will tend to be offset by having trespassed. And you almost have to help them - whether they like it or not - since the alternative is losing IA, which is much worse.
Nope. There is absolutely no consequences to having poor relationship with them, whatsoever. High loyalty gives a small relations bonus (and I assume low loyalty the opposite), but how they feel about you has no impact on loyalty - it is entirely controlled by the events + how you deal with recovered cities (where again - returning a city to someone you have no military access will mean you’re trespassing next round which is just absurd).
They also can’t declare war with you (outside of an event due to low loyalty) from what I could see and you can pretty much control that, as long as you’re not throwing prestige away. So… since loyalty is really the only thing that matters, there’s really no point in wasting prestige on relations. Much better to save it up for handling events, and - eventually - gain the big 10K prestige event (I assume a once-only event, since it never triggered again) which gives you 4 IA or permanent bonuses.
Exploited one elector war to take over Wissenland, but no one liked them anyway - and definitely not a mistake. But other than that, I allowed things to go their course and kept the peace between the electors (who would try to go to war “by event” completely out of sync with their actual relations as well).
As far as I can see, the big problem here is just that they’ve essentially created two relationship mechanics - the normal one, and the “Empire Loyalty” one, with no significant connection between the two. And since the normal relationship mechanic is heavily biased against the player - at least on VH - you very easily end up with a situation where everyone is very loyal, but apparently hates your guts.