Well, I think you are identifying problems and that is the first step to solving them.
I am curious about one other thing. I here about her nights out with E where it is them alone. Where are the nights out with you? You and she a primaries, yes? Then there should be a night each week that is JUST you and her (if possible). Relationships require work.
Maybe something you should ask her is if you and she can for now, subtract one night a week with E and add one with each other.
Would she be interested in trying this? Make it a "no problems allowed" night. Meaning no fighting, no discussing, not arguing, etc.
This is just an idea.
One distinct difference between her connection with you and her conne tion with E is that your connection comes with "real life" attached. And it may be that whAt you two need is a chance to just be a couple instead of two members of a family.
Again, this is just an idea. And i don't know if it is a viable option. But i hope that you can work this all out.